Math 10 - Unit 7 Final Review - Coordinate Geometry
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1 Class: Date: Math 10 - Unit Final Review - Coordinate Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the slope of this line segment. a. b. c. d. 1
2 . Which line segment has slope 4? i) ii) iii) iv) a. iii c. i b. ii d. iv. Determine the slope of the line that passes through G(, ) and H(, 9). a. c. b. d.
3 4. Is the slope of this line segment positive, negative, zero, or not defined? a. zero c. not defined b. positive d. negative. Is the slope of this line segment positive, negative, zero, or not defined? a. positive c. zero b. negative d. not defined
4 6. Is the slope of this line segment positive, negative, zero, or not defined? a. negative c. positive b. not defined d. zero. Is the slope of this line segment positive, negative, zero, or not defined? a. positive c. not defined b. negative d. zero 8. A road rises 9 m for every 60 m measured horizontally. Determine the slope of the road. a. 0 0 c. b. d
5 9. Determine the slope of the line that passes through G(, ) and H( 6, 1). a. 1 b. 1 c. d. 10. A line has x-intercept and y-intercept 6? Determine the slope of the line. 1 a. c. b. d Determine the slope of the line that is perpendicular to this line segment. a. c. 1 b. d. 1
6 1. Determine the slope of the line that is parallel to this line segment. a. b. c. d. 1. Determine the slope of a line that is perpendicular to the line through W( 9, ) and X(6, 10). a. 1 c. 1 1 b The slope of a line is 11. What is the slope of a line that is parallel to this line? 1 d. 1 1 a. b c. 11 d The slope of a line is. What is the slope of a line that is perpendicular to this line? a. c. b. 0 d Determine the slope of a line that is parallel to the line through L( 6, ) and K(1, 9). a. c. b. d. 6
7 1. A line has x-intercept and y-intercept 1. Determine the slope of a line parallel to this line. a. c. b. 1 1 d. 18. A line has x-intercept 4 and y-intercept. Determine the slope of a line perpendicular to this line. a. 4 c. 4 b. 4 d A line has x-intercept and y-intercept. Determine the slope of a line perpendicular to this line. a. c. b. d. 0. The slope of a line is 1. What is the slope of a line that is parallel to this line? a. c. b d. 1. The slope of a line is 1. What is the slope of a line that is perpendicular to this line? a. 14 b. d. c A line passes through J( 10, 10) and K(, 9). Determine the coordinates of L so that line JL is perpendicular to line JK. a. L(, 9) c. L(1, 19) b. L( 19, 1) d. L(9, ). A line passes through D(, ) and N(1, 4). Determine the coordinates of two points on a line parallel to DN. a. (6, 10) and (4, 8) c. ( 10, 6) and (4, 8) b. ( 10, 4) and (6, 8) d. ( 10, 6) and ( 8, 4) 4. A line passes through R(8, 1) and F(, 4). Determine the coordinates of two points on a line perpendicular to RF. a. (16, 11) and (1, ) c. (16, ) and (1, 11) b. (, 16) and (1, 11) d. (16, ) and ( 11, 1)
8 . The slope of this line is. What is the equation of the line? a. y = 1 x + 1 c. y = x + 1 b. y = x + 1 d. y = x Write an equation for the graph of a linear function that has slope 1 and y-intercept. a. y = x 1 c. y = 1 x + b. y = 1 x d. y = x 1 8
9 . Which graph represents the equation y = x + 1? a. c. b. d. 9
10 8. Write an equation to describe this graph. a. y = 1 x 1 c. y = 1 x 1 b. y = 1 x + 1 d. y = 1 x For a service call, a plumber charges a $9 initial fee, plus $4 for each hour he works. Write an equation to represent the total cost, C dollars, for t hours of work. a. t = 4C + 9 c. C = 4t + 9 b. C = 9t + 4 d. C = 4t 9 0. Determine the slope and y-intercept of this graph. a. slope: 4 ; y-intercept: 1. c. slope: ; y-intercept: 1. 4 b. slope: 1.; y-intercept: 4 d. slope: ; y-intercept:
11 1. Write an equation to describe this graph. a. d = t c. d = b. d = t d. d =. Write an equation to describe this graph. a. f(x) = 1 x + 9 c. f(x) = 1 x 9 b. f(x) = 1 x 9 d. f(x) = 1 x + 9. Write an equation for the graph of a linear function that has slope 1 and y-intercept 8. a. y = x + 8 c. y = 8x + 1 b. y = 8x + 1 d. y = x 8 11
12 4. Determine the slope and y-intercept of the graph of this equation: y = x + 9 a. slope: ; y-intercept: 9 c. slope: ; y-intercept: b. slope: 9; y-intercept: d. slope: ; y-intercept:. Use the equation y = x 4 to calculate the value of y when x = 10. a. 4 c. 1 b. 1 d Which equations represent parallel lines? a. y = 8x + 8, y = x + 8 c. y = 8x, y = 14x + 14 b. y = 14x, y = x + 8 d. y = x + 14, y = x + 8. Which equations represent perpendicular lines? a. y = 6x, y = 6x + c. y = 11x, y = 11x + 1 b. y = x + 11, y = 1 x + 6 d. y = 1 x + 6, y = 6x Describe the graph of the linear function with this equation: y + = 1 (x ) a. The graph is a line through (, ) with slope 1. b. The graph is a line through (, ) with slope 1. c. The graph is a line through (, ) with slope 1. d. The graph is a line through (, ) with slope Write an equation for the graph of a linear function that has slope 8 and passes through R(4, ). a. y + = 8(x 4) b. y + = 8(x 4) c. y + = 1 (x 4) 8 d. y = 8(x + 4) 1
13 40. Write an equation for the graph of a linear function that has slope and passes through S( 4, ). a. y + = (x 4) b. y = (x + 4) c. y = (x + 4) d. y = (x + 4) 41. Write an equation in slope-point form for this line. a. y = 1 (x ) c. y = 1 (x ) b. y + = 1 (x + ) d. y + = 1 (x + ) 4. Write this equation in slope-intercept form: y = 1 (x + ) a. y = 1 x + 1 c. y = x + 1 b. y = x + 1 d. y = 1 x Write this equation in slope-intercept form: y = (x + 10) a. y = x + 1 c. y = x + 1 b. y = x + 1 d. y = 1 x + 1
14 44. Determine the y-intercept of the graph of this equation: y = 4(x + ) a. c. b. d Determine the y-intercept of the graph of this equation: y = (x + ) a. 1 c. 10 b. 1 d. 46. Write an equation in slope-point form for the line that passes through A(, 4) and B( 9, 6). a. y 6 = (x + ) c. y 4 = (x + ) b. y + 4 = (x ) d. y + 6 = (x ) 4. Write an equation in slope-point form for the line that passes through A(1, 4) and B(6, 8). a. y + 8 = 4 (x 1) c. y 4 = 4 (x 1) b. y + 4 = 4 (x 1) d. y 8 = 4 (x + 1) 48. Write an equation for the line that passes through T(, ) and is parallel to the line y = x 10. a. y + = 1 (x ) c. y = 1 (x + ) b. y + = (x ) d. y = (x + ) 49. Write an equation for the line that passes through U(, ) and is perpendicular to the line y = 1 x 9. a. y + = 1 (x + ) c. y + = (x ) b. y = (x + ) d. y + = (x ) 0. In which form is the equation x + 6y 8 = 0 written? a. Standard form c. General form b. Slope-intercept form d. Slope-point form 1. Write this equation in general form: y = x + a. x + y = 0 c. x y + = 0 b. x + y + = 0 d. x y = 0. Write this equation in general form: y = x + 8 a. x + y 16 = 0 c. x + y 8 = 0 b. x y + 8 = 0 d. x y 16 = 0 14
15 . Write this equation in general form: y + = (x ) a. x y = 8 c. x y 0 = 0 b. x y 8 = 0 d. x + y 0 = 0 4. Determine the x-intercept and the y-intercept for the graph of this equation: x y + 6 = 0 a. x-intercept: 18; y-intercept: 1 c. x-intercept: 18; y-intercept: 1 b. x-intercept: 18; y-intercept: 1 d. x-intercept: 18; y-intercept: 1. Which equation is written in general form? a. 4x 1y + 1 = 0 c. 1x = 4y 1 b. 1x 4y + 1 = 0 d. 1 x 4y 1 = Determine the slope of the line with this equation: x + y + = 0 a. c. b. d.. Determine the slope of the line with this equation: 16x 4y + = 0 a. 4 c. 1 4 b. 1 4 d Write this equation in slope-intercept form: 10x + y 4 = 0 a. y = 10 x + 4 c. y = 10 x 4 b. y = 10 x + 4 d. y = 10 x 4 1
16 9. Which graph represents the equation 4x 6y 1 = 0? a. c. b. d. 60. Which equation is equivalent to x y 9 = 0? a. y = x + c. y + 1 = (x ) b. y + 1 = (x 6) d. y = (x 6) 61. A line has x-intercept 9 and y-intercept. Determine the equation of the line in general form. a. x + 9y = 0 c. x 9y + = 0 b. x 9y = 0 d. x + 9y + = 0 Short Answer 6. Determine the slope of the line that passes through ( 11, 8) and (6, 16). 6. A 10-ft. ladder leans against a wall. The base of the ladder is on level ground 6 ft. from the wall. What is the slope of the ladder? 16
17 64. The slopes of two lines are 6 11 and 6. Are the two lines parallel, perpendicular, or neither? The slopes of two lines are and 1. Are the two lines parallel, perpendicular, or neither? 66. Are these two line segments parallel, perpendicular, or neither? 6. The coordinates of the endpoints of segments are given below. Are the two line segments parallel, perpendicular, or neither? a) R(, 8), S( 1, 4) and T(, 1), U(9, 4) b) F(, 8), G( 4, 1) and V( 4, 10), W(14, 4) 68. Graph the line with y-intercept and slope. 1
18 69. Write an equation in slope-point form for this line. 0. Write this equation in slope-intercept form: y + = (x ) 1. Write this equation in general form: y = 9 4 x. Write this equation in general form: y = (x + ). Determine the slope of the line of this equation: 9x + y 1 = 0 Problem 4. A guy wire helps to support a tower. One end of the wire is m from the base of the tower. The wire has a slope of 8. How high up the tower does the wire reach?. Write an equation in general form for the line that passes through A(, 4) and B(11, 8). 6. Determine the value of k when the equations kx y 10 = 0 and x + y = 0 represent lines that are: a) parallel b) perpendicular 18
19 Math 10 - Unit Final Review - Coordinate Geometry Answer Section MULTIPLE CHOICE 1. B. C. D 4. C. C 6. A. A 8. D 9. C 10. C 11. D 1. C 1. D 14. A 1. A 16. C 1. D 18. A 19. C 0. C 1. A. D. C 4. C. D 6. B. B 8. A 9. C 0. A 1. A. D. A 4. A. D 6. D. B 8. B 9. B 1
20 40. D 41. A 4. A 4. B 44. C 4. B 46. C 4. C 48. D 49. C 0. C 1. C. A. C 4. D. B 6. A. D 8. B 9. A 60. C 61. C SHORT ANSWER Parallel 6. Perpendicular 66. Neither 6. a) Neither b) Perpendicular
21 y = (x + 4) 0. y = x x 4y 8 = 0. x y + 40 = 0. 9 PROBLEM 4. Sketch a diagram. Slope = rise run The wire is m from the base of the tower, so the run is. The slope is 8. Write an equation. () 8 8 = rise = () rise 00 = rise rise = 40 The guy wire is attached to the building 40 m above the ground.
22 . Since the coordinates of points on the line are known, use this form for the equation of a linear function: y y 1 x x 1 = y y 1 x x 1 Substitute: y 1 = 4, x 1 =, y = 8, and x = 11 Ê ( x ) Ë Á y + 4 x = y + 4 x = 1 8 y + 4 x = y + 4ˆ x = ( x ) y + 4 = x 9 (y + 4) = x 9 y + 8 = x 9 () 0 = x y = x y 1 In general form, an equation that represents the line that passes through A(, 4) and B(11, 8) is: x y 1 = 0 4
23 6. a) Rewrite x + y = 0 in slope-intercept form. x + y = 0 y = x y = x From the equation, the slope of the line is. Rewrite kx y 10 = 0 in slope-intercept form. kx y 10 = 0 y 10 = kx y = kx + 10 y = k x 10 From the equation, the slope of the line is k. Any line parallel to y = x has slope. k So, = () k = () k = 14 k = 14 When the lines are parallel, k is 14. b) Any line perpendicular to y = x has a slope that is the negative reciprocal of ; that is, its slope is 1. k So, = 1 () k = 1 () k = k = 6 When the lines are perpendicular, k is 6.
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