Geometry Coordinate Geometry & Transformations 3 — Questions and Answers
Question 1: A figure is rotated 90 degrees counterclockwise about the origin. Point (2, 3) maps to?
- (-3, 2) (Correct answer)
- (3, -2)
- (-2, -3)
- (3, 2)
Correct answer: (-3, 2)
A 90 degree CCW rotation maps (x, y) to (-y, x), giving (-3, 2).
Question 2: Which lines are parallel?
- y = 2x + 1 and y = 2x - 4 (Correct answer)
- y = 2x and y = -2x
- y = 3x and y = x/3
- y = x + 1 and y = -x + 1
Correct answer: y = 2x + 1 and y = 2x - 4
Parallel lines have equal slopes; both have slope 2.
Question 3: Two lines are perpendicular if their slopes are 3 and what value?
- -1/3 (Correct answer)
- 3
- 1/3
- -3
Correct answer: -1/3
Perpendicular slopes are negative reciprocals, so -1/3.
Question 4: A dilation with scale factor 3 centered at the origin maps (2, -1) to?
- (6, -3) (Correct answer)
- (5, 2)
- (2/3, -1/3)
- (6, 3)
Correct answer: (6, -3)
Multiply each coordinate by 3: (6, -3).
Question 5: What is the length of the segment from (-3, 0) to (3, 0)?
- 6 (Correct answer)
- 0
- 3
- 9
Correct answer: 6
The horizontal distance is |3 - (-3)| = 6.
Question 6: Reflecting (4, 5) across the line y = x gives?
- (5, 4) (Correct answer)
- (-4, -5)
- (-5, -4)
- (4, -5)
Correct answer: (5, 4)
Reflection across y = x swaps the coordinates to (5, 4).
Question 7: What is the y-intercept of the line 2x + 3y = 12?
- 4 (Correct answer)
- 6
- 12
- -4
Correct answer: 4
Set x = 0: 3y = 12, so y = 4.
Geometry Coordinate Geometry & Transformations 3
A figure is rotated 90 degrees counterclockwise about the origin.
Point (2, 3) maps to?