Parallel and Perpendicular Lines Multiple Choice Identify the choice that best completes the statement or answers the question. ____
1. Which angles are corresponding angles?
a. b. ____
∠8 and ∠16 ∠7 and ∠8
c. d.
∠4 and ∠8 none of these
2. Find the values of x and y. The diagram is not to scale.
a. b.
x = 77, y = 59 x = 77, y = 57
c. d.
x = 57, y = 77 x = 41, y = 57
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3. Complete the statement. If a transversal intersects two parallel lines, then ____. a. corresponding angles are supplementary b. same-side interior angles are complementary c. alternate interior angles are congruent d. none of these
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4. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary. a. acute c. same-side interior b. alternate interior d. corresponding
1
Name: ________________________ ____
ID: A
5. Find m∠Q. The diagram is not to scale.
a.
60
b.
120
c.
110
d.
70
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.
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6. How are ∠6 and ∠2 related? a. corresponding angles b. alternate interior angles
c. d.
same-side interior angles none of these
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7. Write an equation in point-slope form of the line through points ( 4, –4) and (1, 2). Use (4, –4) as the point (x1, y1). a. (y – 4) = –2(x + 4) c. (y + 4) = 2(x – 4) d. (y + 4) = –2(x – 4) b. (y – 4) = 2(x + 4)
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8. Write an equation for the horizontal line that contains point E(–3, –1). a. x = –1 b. x = –3 c. y = –1 d.
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y = –3
9. Write an equation in slope-intercept form of the line through points S(–10, –3) and T(–1, 1). 4 13 4 13 a. y = − x + c. y = − x – 9 9 9 9 4 13 4 13 b. y = x – d. y = x + 9 9 9 9 2
Name: ________________________
ID: A
____ 10. At the curb a ramp is 11 inches off the ground. The other end of the ramp rests on the street 55 inches straight out from the curb. Write a linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb. 1 c. y = − x + 55 a. y = 5x + 11 5 1 1 b. y = − x + 11 d. y = x + 55 5 5 ____ 11. Write an equation for the line parallel to y = –7x + 15 that contains P(9, –6). c. y – 6 = –7(x – 9) a. x + 6 = 7(y – 9) b. y + 6 = 7(x – 9) d. y + 6 = –7(x – 9) ____ 12. Write an equation for the line perpendicular to y = 2x – 5 that contains (–9, 6). 1 a. y – 6 = 2(x + 9) c. y – 9 = − (x + 6) 2 1 b. x – 6 = 2(y + 9) d. y – 6 = − (x + 9) 2 ____ 13. Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = 3x – 3. A perpendicular brace passes through the point ( –7, 9). Write an equation of the line that contains the brace. 1 a. y – 7 = (x + 9) c. x – 9 = 3(y + 7) 3 1 b. y – 9 = 3(x + 7) d. y – 9 = − (x + 7) 3 ____ 14. What must be true about the slopes of two perpendicular lines, neither of which is vertical? a. The slopes are equal. b. The slopes have product 1. c. The slopes have product –1. d. One of the slopes must be 0. ____ 15. Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain. a. Yes; their slopes have product –1. b. No; their slopes are not opposite reciprocals. c. Yes; their slopes are equal. d. No; their slopes are not equal ____ 16. Give the slope-intercept form of the equation of the line that is perpendicular to 7x + 3y = 18 and contains P(6, 8). 3 3 38 a. y – 6 = (x – 8) c. y = x + 7 7 7 3 18 3 b. y = x + d. y – 8 = (x – 6) 7 7 7
