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Unit: Coordinate Geometry Name ________________________ Dates Taught _________________ General Outcome 10I.R.3Demonstrate an understanding of slope Parallel and Perpendicular Lines Graphing using Slope-Intercept10I.R.4Describe and represent linear relations using: Table of Values Graphs Equations10I.R.5Determine the characteristics of the graphs of linear relations, including the Slope Intercepts 10I.R.6Linear Relations expressed in different forms. 10I.R.7Determining the Equations a linear relation, given: a graph a point and the slope 2 Points Parallel and Perpendicular Lines10I.R.10 Distance between Two Points Outcome:10I.R.10 Midpoint of a Segment Comments : ________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ Review: Graphing Points Coordinate axes consist of a horizontal and a vertical number line crossing at zero. The horizontal axis is called the axis and the vertical axis is called the axis. The plane is divided into regions called quadrants. The quadrants are numbered as shown. The numbering of the quadrants starts at the upper right and proceeds counter clockwise around the origin. Points are designated by an ordered pair of numbers called coordinates. The number of the pair is the x-coordinate. The second number of the pair is the -coordinate. The coordinates of the origin are ( , ).  Example: Determine the coordinate of the following points. A B C D Example: Graph and label the following points. G (-5, -2) H (4, 0) I (2, -4) J (0, -3) Example: Determine the quadrant of the following points. A B C D E F Homework: Graphing Points 1. Write the coordinates of the following points. A _________ B _________ C _________ D _________ E _________ F _________  2. Graph and Label the following Points G ( 7, 1) H (-4, 2) J (5, 0) K ( -5, -8) L (6, -1) M (2, 0) 3. Give the quadrant for the following points. (-2, 8) __________ (5, -1) __________ (-3, -7) ________ Outcome:10I.R.10 - Distance Between Two Points There are possibilities where we may need to find the distance between points on a coordinate plane. The distance between and pairs of points is trivial. We can simply the between the two points.  Examples: Find the distance between A(-3, 7) and B(6, 7). Find the distance between C(6, -4) and D(6, 6). When a line segment is diagonal, you are not able to simple count the distance. Based on the Pythagorean Theorem, we are able to determine the diagonal distance between two points. The length of a line segment is determined by following formula, called the Distance Formula:  Example: Find the distance between the points (-7, 5) and (4, -3). Let ( , ) = (-7, 5) and ( , ) = (4,-3). ( Substitute the values of these points into the Distance Formula and solve.  Example: Find the distance between (-12, 15) and (8, 3) using the distance formula. Example: A quadrilateral has vertices P(3, 5), Q(-4, 3), R(-3, -2), and S(5, -4). Find the lengths of the diagonals, to the nearest tenth.  Homework: Distance Homework (page 8) Outcome:10I.R.10 Midpoint of a Segment Midpoint of a line segment is the exact middle spot between the endpoints. To find the midpoint between points, we can apply the Midpoint Formula.  The midpoint is simply the of the coordinates of the two points. Examples: Find the midpoint between A(-3, 7) and B(6, 7).  Find the midpoint between C(7, -4) and D(7, 6). Find the midpoint between E(0, 3) and F(4, -5). Find the midpoint between G(-8, 2) and H(-3, -6) Example: The endpoints of PQ are P(3, -4) and Q(11, c). The midpoint of PQ is M(d, 3). Find the coordinates of c and d. Example: The center of circle has coordinates (-1, -3). One endpoint of a diameter of the circle has coordinates (-3, 0). What are the coordinates of the other endpoint of the diameter? Homework: Midpoint Homework (page 11) Distance Homework  1. Find the distance between the following pairs of points to two decimal places. Show your work. Example: A and B (2, 6) and (6, -1)  EMBED Equation.DSMT4  16 + 49 = 65  EMBED Equation.DSMT4  B and C C and D c) A and D d) B and D e) A and C 2. Bob and Christine want to get together (see map below). Each block is 120 m by 120 m. Assuming the roads are of negligible width, how far does Bob have to travel to reach Christine if: he is restricted to the roads? he can follow a direct path?  3. Three vertices of a rectangle ABCD are given: A(-3, 1) B(2, 1) C(-3, 5) a) Determine the coordinates of vertex D. b) Find the lengths of the sides. c) Determine the length of the diagonal. 4. A triangle has vertices of A(-2, 5), B(5, 3), and C(0, 2). Find the perimeter of triangle ABC. Classify the triangle as scalene (no equal sides), isosceles (two equal sides), or equilateral (three equal sides).  5. P is the point (4, 2). Q is a point on the y-axis so that PQ = 5. Find the possible coordinates of Q (two answers).  6. Given the following graph of a line, which of the points (0, 5), (3, 4), (2, 1), (1, 3), (5, -5) and (-1, 7) do not lie on the line? Midpoint Homework 1. Find the midpoint of the following pairs of points. Show your work. Example: A and B  EMBED Equation.DSMT4  B and C C and D c) A and D d) B and D e) A and C 2. The midpoint of AB is the origin. B has coordinates of (3, 7). What are the coordinates of A? 3. One endpoint of a segment AB is A(-3, 6). If the coordinates of the midpoint are (1, 2), find the coordinates of B. 4. The endpoints of the diameter of a circle are (-6, -2) and (2, 4). Find the circumference and area of the circle correct to three decimal places.  EMBED Equation.DSMT4  5. A(1, 1), B(7, 3), C(8, 6) and D(2, 4) are the vertices of parallelogram ABCD. Find the midpoint of AC and the midpoint of BD. Comment on your result. Outcome 10I.R.4: (Graphing Lines) Table of Values One of the simplest ways of finding points to graph the equation of a line is by creating a table of listing the ordered pairs ( , ) that the equation. A minimum of points is needed: points determine a line while the and others can be used to the first two. Example: Graph the following equations using a table of values. y = 3x + 1xy y = -6xySteps: 1) Isolate for . 2) Pick at least values for x. (choose numbers). 3) Substitute the x-values in the equation and calculate . 4) Graph each point. Join using a . x = 8xy For Example: Graph the following equations using a table of values. 2x + y = 4xy y = -2/3x - 4xy  5x + 2y = 10xy 2x - 3y - 6 = 0xy Homework: Exercise 6 (MCAL20S) Outcome 10I.R.5: Slope The of a line or segment is a measure of how that line is. It also tells the of the line. Slope can also represent a such as kilometres over time (km/h). There are possible types of slopes (Imagine skiing from left to right):    Horizontal vertical Positive (up) Negative (down) Zero (no slope) Undefined (impossible) Another way of thinking about slope is measuring the distance a segment (or ) over a distance called the . In other words slope is found by the change by the change. It is usually represented as a fraction. Example: Determine the rise and run for each line segment. Then, find the slope.  Y11 D10987 6 E C5432 1X-11-10-9-8-7-6-5-4-3-2-101234567891011 A-1 -2 F-3-4-5-6-7 GH -8 B-9-10-11 Example: Use the slope formula to find the slopes of the line segments with endpoints given below. a) A(2, 1), B(5, 3) b) C(-3, 4), D(-1, -2) c) G(4, -2), H(5, 4) d) M(1, -2), N(1, 3) Example: The slope of a line is 2. The line passes through (-1, k) and (4, 8). Find the value of k. Example: The slope of a line is -1/2. The line passes through (10, r) and (2, 3). Find the value of r. Homework: Unit 6.5, Pg. 132 #1-4, 6 Outcome 10I.R.5: Graphing using x & y Intercepts An intercept is the where the line the or axis. The ____________ is the point where the line ___________ the x-axis. At the , the value of y is always . The ____________ is the point where the line crosses the ___________. At the , the value of x is always . To determine these intercepts, we find the when , and the . when . Then we these two points (intercepts) and them to draw the line. Example 1: A) Use the intercept method to graph 3x - 4y = 12.  Step 1:To find the x-intercept, let y = 0: 3x - 4y = 12 x = (The x-intercept is (____, ____). Step2:To find the y-intercept, let x = 0: 3x 4y = 12 y = . (The y-intercept is (____, ____). Step 3: Plot these points (intercepts) on the graph, and join the points with a line. Example 2: B) Use the intercept method to graph 5x - 4y + 20 = 0. To find the x-intercept, To find the y-intercept, x = ____ y = ____ The x-intercept is The y-intercept is Example 3: C) Use the intercept method to graph  EMBED Equation.3  below. x-intercept: y-intercept:  Example 4: D) Graph 5x + 6y = -30 using the intercept method. What is the slope of this line? Homework: Exercise 11 (MCAL20S) Outcome 10I.R.3: Graphing using Slope-Intercept . of lines can be written in what is called the form of , where represents the of the line. ( over .) represents the of the line. (line the -axis.) Examples: Graph and label the following lines: ( A line with a slope of -3 and a y-intercept of 6. ( A line with a slope of 2/3 and a y-intercept of -5. ( A line with no slope and a y-intercept of 7. ( A line with an undefined slope and an x-intercept of -6. To use slope-intercept form, the equation of the line be in form. If they are not, they must be using algebra. To convert, everything in the equation, the variable, must be to the side, and the y should have a of . Using these two variables, a line can be graphed in steps as follows: ( . the equation to y = mx + b form. ( Interpret the as the , and on the y-axis. ( From the , count off units as indicated in the , remembering that the slope is a fraction ( / ). (+Rise = , - rise = +run = , -run = ) ( . the two points with a line.  Example: Graph and label the following equations, using the slope-intercept method. y = (3/4)x + 2. y = -5x + 8. Examples: Find the slope and y-intercept of the following lines and plot: 3. 5x + 2y = 10  Slope =______________ Y-intercept = __________ 4. 2x - 3y - 6 = 0 Slope = ______________ Y-intercept = __________ Homework: Exercise 12 (MCAL20S) Outcome 10I.R.7: Determining the Equations of Lines Using Slope-Intercept & Slope-Point Methods A) Slope-Intercept Method: Recall that the slope-intercept form is where m is the , and b is the . Therefore, when given the slope and y-intercept of a line, creating the . is only a matter of . Examples: 1) Given the slope is 2 and the y-intercept is 3, what is the equation of the line? 2) Given the slope is 1/2 and the y-intercept is -5, what is the equation of the line? 3) Given m = -0.5 and b =1/3, what is the equation of the line? 4) Given m = -5 and b = 0, what is the equation of the line? B) Slope-Point Method: To find the equation of a line using the and a (not the y-intercept), start by using the y = mx + b formula for lines. ( the value for , and the and coordinates from the given point into the y = mx + b form of the equation. for b. ( Then simply the equation in y = mx + b form, the values for (slope) and (y-intercept). Example: Find the equation of the line that passes through (1, 4) with slope m = 3. The equation in y = mx + b form is _____________________________________. Example: Find the equation of the line that passes through (-4, -2) with slope m = 2/3. The equation in y = mx + b form is _____________________________________. Example: Find the equation of the line that passes through (3, -6) with slope m = -3. The equation in y = mx + b form is _____________________________________. Homework: Exercise 13 (MCAL20S) and Unit 7.1 (Slope-Intercept Form) #1-4 Outcome 10I.R.6: Forms of Equations of Lines Equation of lines can be written in many ways. The following are the 2 most common formats: 1) Slope intercept form: y = mx + b The slope is represented by The y-intercept is represented by Ex: y = 2x + 2 y = -1/3x + 5 y = x 7 Make your own example 2) Standard form: Ax + By + C = 0 One side of the equation must equal to No fractions or Ex: 2x - y + 2 = 0 0 = x + 3y - 15 2y - x + 7 = 0 Make your own example Example: Convert the following to slope-intercept form.  EMBED Equation.3  b)  EMBED Equation.3  Example: Convert the following to standard form.  EMBED Equation.3  b)  EMBED Equation.3   EMBED Equation.3  d)  EMBED Equation.3  Homework: Unit 7.2 (General Form) Practice Converting Equations of Lines Slope Intercept form ( Standard form y = mx + b ( Ax + By + C = 0 Convert the following equations to the both of the above forms: Graph each line. 1. y = 4x + 8 2. 3y = 7x 9 3. 4y = -8x + 16 4. 10x = 5y + 25 5. 3y 8x = 10 6. 12 4x = 8y 7. 4x + 2y 2 = 0 8. -9y 3x = 2 9. 2x = 3y 10.  EMBED Equation.3  Answers: 1. y = 4x+8; 4x-y+8=0 2.  EMBED Equation.3 ; 7x-3y-9=0; 3. y=-2x+4; 2x+y-4=0 4. y=2x-5; 2x-y-5=0 5.  EMBED Equation.3 ; 8x-3y+10=0 10. y = x/2 2/3; 3x 6y 4 = 0 Outcome 10I.R.7: Determining Equations of Lines Using 2 Points & Standard Form  To find the equation of a line given , we begin by finding the using the slope formula: Once we know the slope, we can it into the form of the equation ( ) and solve for . Equations of lines can also be written in of Ax + By +C = 0, where A, B, and C are . Equations can be transposed into standard form by using simple algebra. Example: Convert the equation y =  EMBED Equation.3 x + 5 into Standard Form. Example: Find the equation for the line that passes through the points (-2, 3) and (2, -5). Solution: Use the to find the . . the above value for (m) into y = mx + b. . the of one of the above into y = mx + b and for . . the equation in y = mx + b form. 5. . the equation into Form. Example: Find the equation for the line that passes through the points (3, 4) and (4, 6). Solution: 1. Use points ( slope. 2 & 3. Use m & (x, y) to solve for b. 4. y = mx + b form: 5. ( Standard Form. Example: Find the equation for the line that passes through the points (1.5, 2) and (-1.5, -7). Solution: Homework: Exercise 15 (MCAL20S) Outcome 10I.R.7: Determining Equations From a Graph of a Line . lines have equations like . . lines have equations like . To find the equations of lines in y = mx + b form, you need the and . The can be found from on the graph of the line. The may be found on the , or it may need to be calculated by the of one of the points into y =mx + b. Example: Find the equations of the following lines (slope-intercept & standard forms) from the graphs.  Y1161098176542321X-11-10-9-8-7-6-5-4-3-2-101234567891011-1-2-33-45-5-6-74-8-9-10-11 Outcomes 10I.R.3 & 10I.R.7: Parallel and Perpendicular Lines A) Graph the following lines below using the slope-intercept (y = mx + b) method. y = 3x - 2 ( What is the same about these lines equations? ( y = 3x - 5 ( What is different in each of these lines equation? ( 9x - 3y + 24 = 0 ( What can you summarize about parallel lines? Give some equations of other pairs of parallel lines. ______________________________ B) Graph the following lines below using the slope-intercept (y = mx + b) method.  ( y = 3x - 6 ( What do you notice about these lines? ( What do you notice about ( y = -1/3x + 2 the slopes of these lines equations? ( y - 1/2x =5 ( What can you summarize about perpendicular lines? ( 2x + y - 7 = 0 ( Give some equations of other pairs of perpendicular lines. ___________________________________ Example: Write a standard form of the equation of a line that runs through the point (-2, 3) and is parallel to the line 5x - y + 12 = 0. the line equation to y = mx + b form. ( m = . The equation of the new parallel line will have a slope of . the and the of the point into the slope-intercept form of the equation and for . Write the new equation in slope-intercept form (y = mx + b), using and . the equation to . (Ax + By + C = 0) Example: Given a line that passes through A(-2, 5) and B(6, 4). Determine the slope of a: a) parallel line. b) perpendicular line. Example: Are the following lines parallel, perpendicular or neither? a) y = 2x 7 and 4x 2y + 8 = 0 b) 2x 3y 3 = 0 and 3x + 2y 4 = 0 Example: Write the equation of a line perpendicular to the line 2x - 3y + 1 = 0, and passing through the point (1, 2). Homework: Unit 7.4 (Parallel and Perpendicular Lines) Graphing Lines Using the TI-83 Graphing Calculator Buttons we will be using:  To graph the line, our equation must be in _____________ form.   To enter x (independent variable). This sets the parameters of the graph. x-min = x-max= x-scl = 1 y-min = y-max= y-scl = 1   or 2nd graph Shows the table of values for the graph  or 2nd Window Allows us to choose the stating x-value and the scale the table goes up by.  Shows the graph.  Use the < or > buttons to move along the graph. This gives exact coordinate points.  Zooms in or out. (Zstandard gets back to original parameters) If an Error occurs: 1) Remember to check x/y-min = -10 x/y max = 10 x/y scl = 1 2) Check to see if your stats plot is off.   or 2nd y= Enter 4 ENTER 3) Know the difference between your (-) and - buttons. 4) Also check or 2nd zoom  Choose: RectGC CoordOn GridOff AxesOn LabelOff ExprOn Example 1 Using your TI-83, graph the following equations. Make a sketch of each graph. a) y = x + 2 b) 2y 10x = 10 c) 5x y = -11 To find your y intercepts on the TI-83: Recall, the ___________ (___) is found algebraically by letting x = ____ and solving for your y-value. On the graphing calculator,  or 2nd TRACE -Then Value (or press 1) Put X=0 and press ENTER To find your x intercepts on the TI-83: Recall, the x-intercept (also called ___________) is found algebraically by letting y = ____ and solving for your x-value. On the graphing calculator,  or 2nd TRACE -Then zero (or press 2)  -Left Bound? Use the < and > buttons Put the curser left of the x-intercept. ENTER -Right Bound? Use the < and > buttons Put the curser right of the x-intercept ENTER -Guess? Use the < and > buttons Put the curser on the x-intercept ENTER Example 2 Using your graphing calculator, graph the following equations. Indicate the y-intercept and x-intercept. y = x + 1 2x 3y = 8 Homework:     PAGE  Intro to Applied and PreCalc Notes Unit: Coordinate Geometry PAGE  Page  PAGE \* MERGEFORMAT 32 87654321-7-6-5-4-3-2-101234567-1-2-3-4-5-6-7 d =  EMBED Equation.3  d =  EMBED Equation.3  87654321-7-6-5-4-3-2-101234567-1-2-3-4-5-6-7 Midpoint (x, y) =  EMBED Equation.3  87654321-7-6-5-4-3-2-101234567-1-2-3-4-5-6-7 87654321-8-7-6-5-4-3-2-1012345678-1-2-3-4-5-6-7 87654321-7-6-5-4-3-2-101234567-1-2-3-4-5-6-7 87654321-7-6-5-4-3-2-101234567-1-2-3-4-5-6-7 Slope = m = EMBED Equation.3  AB = CD = EF = GH = 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 Slope (m) =  EMBED Equation.3  Line 1: Line 2: Line 3: Line 4: Line 5: Line 6: Homework: Unit 7.1 (Slope-Intercept Form) #5 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 8765432-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7 87654321-7 -6 -5 -4 -3 -2 -101234567-1-2-3-4-5-6-7    !abrw~Ʒpe^VeNC5h h 6OJQJ]h h OJQJh OJQJhb;;OJQJ h+h+h&fh+OJQJh+hpCJOJQJaJhphpCJOJQJaJhphpOJQJhAXhpCJ OJQJaJ hAXhpCJHOJQJaJHhAXh+CJHOJQJaJHhAXhPZCJHOJQJaJHhAXhPZ>*CJHOJQJaJHhphc<OJQJhc<OJQJhpOJQJ !`brstuv $Ifgdp$a$gdpgdpvw]TG:: & F$Ifgd  & F$Ifgd $Ifgd+kd$$Ifl\: &L t044 laytp / 5 6 ? @ C J K E M ˪旉td\h OJQJh+hp5>*OJQJaJh 5>*OJQJaJhpOJQJh&fh+6OJQJ]h+OJQJhphpOJQJh&fh+OJQJhphOJQJh/h/OJQJh/OJQJh&fhOJQJhOJQJhph+OJQJh+h hPZOJQJ / WNE8 & F$Ifgd $Ifgd $Ifgdpkd$$Ifl\: &L t044 laytp$If/ 6 @ A B C K :kdB$$Ifl\: &L t044 laytp $Ifgdp & F$Ifgd/ & F$IfgdK >kd$$Ifl\: &L t044 laytp $Ifgdp & F$Ifgd $Ifgd/ Gkd$$Ifl\: &L t044 laytp  & F$Ifgd $Ifgdp ' / E N o p q $Ifgdp & F$Ifgd  & F$Ifgd $Ifgd M N n o r z | ²rgYNNC4hphpCJOJQJaJhphPZOJQJh+hPZmH sH h+hPZ6OJQJ]h+hPZOJQJh+hPZ0JOJQJhPZ56>*OJQJ]aJhAX56>*OJQJ]aJ$h+hPZ56>*OJQJ]aJh+hPZ5>*OJQJaJ"h+hPZ0J5>*OJQJaJhphpOJQJhph+OJQJh&fh+OJQJh h+OJQJq r | ]TG:T & F$Ifgd  & F$Ifgd $Ifgdkd%$$Ifl\: &L t044 laytp   A B RMMMMMMgdpkd$$Ifl\: &L t044 layt $IfgdB 0 1  ; Z [  h`hgdM & F gdM & F gdMgdMgdp S X 8@BJMNPZhϿϿϦϿϿϿϿϿύ}o`PPhphc->*CJOJQJaJhphc-CJOJQJaJhphMCJOJQJ\hphM5CJOJQJ\0jhph=.CJOJQJUaJmHnHu0jhphMCJOJQJUaJmHnHuhphM>*CJOJQJaJhphMCJOJQJaJhphM5CJ OJQJaJ "hphM5>*CJ OJQJaJ MOP=>HTU_z{gd5vgdc-gdM & F gdM6;<>?@BEGHInZnZF3$hphtB/CJOJQJaJmH sH 'hphM>*CJOJQJaJmH sH 'hphtB/>*CJOJQJaJmH sH $hphtB/CJOJQJaJmH sH $hphMCJOJQJaJmH sH hphtB/CJOJQJaJhphc-CJOJQJaJhphc-CJOJQJ\hphc-5CJOJQJ\hphM>*CJOJQJaJhphMCJOJQJaJhph=.>*CJOJQJaJIJKMQSTUVWY\^_`hz{|  ƲƣtbR990jhphMCJOJQJUaJmHnHuhph5v5CJ OJQJaJ "hph5v5>*CJ OJQJaJ hphM>*CJOJQJaJhphtB/>*CJOJQJaJhphtB/CJOJQJaJhphMCJOJQJaJ'hphM>*CJOJQJaJmH sH 'hphtB/>*CJOJQJaJmH sH $hphtB/CJOJQJaJmH sH $hphMCJOJQJaJmH sH   45@ALMWXdepqz{|gdM|}~ %&VWXYZ & F !h^h ! & F h^hgdg,gdM *<Ѱ~qcqcqcqcqcqK/jhph:5CJOJQJUmHnHuhph:>*CJOJQJhph:CJOJQJhph:CJ OJQJaJ %hph:6>*CJ OJQJ]aJ hphg,>*CJ OJQJaJ hph:>*CJ OJQJaJ hph!9n0JCJ OJQJaJ hphg,0JCJ OJQJaJ hphMCJOJQJaJhph5vCJOJQJaJ#&@HMUt|%/012<aq~յյբՋ~qaյյShphes5CJOJQJ jhph:CJOJQJhphesCJOJQJhph:CJOJQJ,jhph:CJOJQJUmHnHu$hph:56CJOJQJ\]hph:6CJOJQJ]hph:5CJOJQJ\hph:CJOJQJhph:5CJOJQJhph:5>*CJOJQJ./0~  !`  & F ! ! $ !a$ v{}~پ˱ziYJ>hRkCJOJQJaJh&h CJOJQJaJh h >*CJOJQJaJ hphesCJOJQJmH sH hphes5>*CJOJQJ,jhphesCJOJQJUmHnHuhphes6CJOJQJ]hphesCJOJQJhph:CJOJQJhphes5CJOJQJhph:5CJOJQJ/jhphes5CJOJQJUmHnHu}gdes !0^`0gdes  !gdes !1 & F h^h !gdesNRl|w^N>hph:5>*CJOJQJhph:6CJOJQJ]0jhph:CJOJQJUmHnHsH uhph:5CJOJQJ\hph:>*CJOJQJhph:CJOJQJhph:CJ OJQJ!hph:6>*CJ OJQJ]hph:>*CJ OJQJhphg,>*CJ OJQJaJ hph!9n0JCJ OJQJaJ hphg,0JCJ OJQJaJ    (05=>@A\chquz1AJX^ǰǠǠǒxpeh h mH sH h mH sH h CJOJQJhph:6CJOJQJ]hph*m5CJOJQJhph*m5CJOJQJ\,jhph:CJOJQJUmHnHuhph*mCJOJQJhph:5CJOJQJ\hph:CJOJQJhph:5CJOJQJ'    >?@ABrstuvwxyz{  !gd*m !123456789:;<=>?@A ! !0^`0gd*m $ !a$gd*m !0^`0     8:Mgdgd  !gdRkgd gd !78:CKLMN˾m^L@^@^h7mCJOJQJaJ"h7mh5>*CJOJQJaJh7mhCJOJQJaJ0jh7mhCJOJQJUaJmHnHuh7mh7m5CJOJQJaJ"h7mh7m5>*CJOJQJaJ"h7mh5>*CJOJQJaJhhphRkCJOJQJhRkCJOJQJaJh&hRkCJOJQJaJh hRk>*CJOJQJaJh CJOJQJMO *+9:;<=>?@cdefg  & F hgd7m hgdgd&'()+,@ARVouDzݜ{{{{{o`Uh7mh7mOJQJh7mh7mCJOJQJaJhCJOJQJaJh7mCJOJQJaJ)jGh7mhCJEHOJQJUaJ+j7iK h7mhCJOJQJUVaJ)jkh7mhCJEHOJQJUaJ+j,iK h7mhCJOJQJUVaJh7mhCJOJQJaJ%jh7mhCJOJQJUaJghklmoCijgd7m hgdwyz{|   ȹk_Ph7mhCJOJQJaJh7mCJOJQJaJ0jh7mhCJOJQJUaJmHnHu$h7mhCJOJQJaJmH sH h7mh7m5CJOJQJaJ"h7mh7m5>*CJOJQJaJh7m5>*CJOJQJaJh7mCJOJQJaJmH sH h7mh7mOJQJh7mOJQJ(jh7mh7mOJQJUmHnHu345XYZ&Qtuvwxy{gd7m  4_ hgdgd7mgd7m*+,-.JKXYZ[\]^  & F hgd7m hgd./FGHIos ! 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"2(9/<|,`!(9/<|  @ sxڕJAgs ԀX)l`&$p!M#RHe"O"V*,DE%f1=nc9䁏nXr%DAXk5%B㝡I\6]+i%1s4Pw|9*daگC{>H"tuЋzЛO%ROҎC ɇR߲I>s _/~{XO2Z>#>U}Vl'N#tcvw:sp_إRJd2p7/%{b9coRӶoGٌ$5 "Qn`vzG}>wm $$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd`$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdع$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdP$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd@$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akd0$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akd$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  4akdX$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdH$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd8$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd($$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kdd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd($$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kdt$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd8$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /  /  / /  4a-kd$$If֐<\|  <\|                                     0HHHHa$$If!vh#v :V 05 /  /  / /  4a-kd$$If֐<\|  <\|                                     0HHHHa$$If!vh#v :V 05 /   / 4a-kd $$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kdD$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kd$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /   / 4a-kdT#$$If֐<\|  <\|                   0HHHHa$$If!vh#v :V 05 /  /  4akd'$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd*$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd.$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd1$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd4$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdp8$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd;$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akd`?$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akdB$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  4akdF$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdJ$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdxM$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdP$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdhT$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdW$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdX[$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd^$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdHb$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akde$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd8i$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdl$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd(p$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akds$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akdw$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akdz$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  4akd@~$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd0$$IfdObjInfo]Equation Native _1118002240`F`M`MOle un=y 2 "y 1 ()x 2 "x 1 () FMicrosoft Equation 3.0 DS Equation Equation.39q،mIyI riserYZ<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd $$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a}Dd @kzJ  C A? "2|Xd S ̖,`!|Xd S Ê @pxڥSAKA~ͮR !ꠠK:VRFyC_DW/xT6vvS EA SNTdIA}3y\LPRT2^fl W"p$~O+(ԜU;n^YvaP}J;sU;2N4-BB)^鈽S]KQaQ@OZb`fƇ`Ț3MUw!JTTgGwpĕ6)s[ߔwu]יs_⌆w Qmw\`~xV$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd}$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdm$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd]$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdխ$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akdM$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  /  /  4akd$$Ifd<\|  <\|                                 0@@@@a$$If!vh#v :V 05 /  /  4akdu$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akde$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd$$Ifd<\|  <\|          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0@@@@a$$If!vh#v :V 05 /  /  4akdc$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdf$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdj$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd}m$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdp$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdmt$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdw$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd]{$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd~$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akdM$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 0CompObj_afObjInfobEquation Native 1Table\8un=y 2 "y 1 x 2 "x 1Oh+'0 ( H T ` lxCoordinate GeometryKim RodstromNormal Ken Krahn43Microsoft Office Word@      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWX]^_`abcdefghijklmnopqrstuvwxyz{|}~5 /  /  4akdŅ$$Ifd<\|  <\|                 0@@@@a$$If!vh#v :V 05 /  /  4akd=$$Ifd<\|  <\|              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