College Math Placement Test Coordinate Geometry 2 — Questions and Answers
Question 1: Which pair of lines is parallel?
- y = 2x + 1 and y = −2x + 1
- y = 3x + 2 and y = 3x − 5 (Correct answer)
- y = x + 4 and y = 2x + 4
- y = −x + 3 and y = x + 3
Correct answer: y = 3x + 2 and y = 3x − 5
Parallel lines have equal slopes; both y = 3x + 2 and y = 3x − 5 have slope 3.
Question 2: Which pair of lines is perpendicular?
- y = 2x + 1 and y = 2x − 3
- y = 3x + 1 and y = 3x + 5
- y = 4x − 1 and y = −¼x + 2 (Correct answer)
- y = x + 2 and y = x − 4
Correct answer: y = 4x − 1 and y = −¼x + 2
Perpendicular lines have slopes that are negative reciprocals; 4 × (−¼) = −1.
Question 3: What is the x-intercept of the line y = 3x − 9?
- x = 2
- x = 3 (Correct answer)
- x = −3
- x = 9
Correct answer: x = 3
Set y = 0: 0 = 3x − 9, so 3x = 9 and x = 3.
Question 4: What is the distance from the origin to the point (5, 12)?
- 17
- 13 (Correct answer)
- 15
- 11
Correct answer: 13
Distance = √(5² + 12²) = √(25 + 144) = √169 = 13.
Question 5: What is the midpoint of the segment from (−4, 3) to (6, −1)?
- (1, 1) (Correct answer)
- (2, 1)
- (1, 2)
- (0, 1)
Correct answer: (1, 1)
Midpoint = ((−4+6)/2, (3+(−1))/2) = (2/2, 2/2) = (1, 1).
Question 6: What is the slope of any horizontal line?
- 1
- Undefined
- −1
- 0 (Correct answer)
Correct answer: 0
Horizontal lines have no rise, so rise/run = 0/run = 0.
Question 7: What is the equation of the vertical line passing through (4, −2)?
- y = 4
- x = −2
- x = 4 (Correct answer)
- y = −2
Correct answer: x = 4
Vertical lines have equations of the form x = constant; here all points share x = 4.
College Math Placement Test Coordinate Geometry 2
Which pair of lines is parallel?