Geometry Coordinate Geometry & Transformations 2 — Questions and Answers
Question 1: What is the distance between points (1, 2) and (4, 6)?
- 5 (Correct answer)
- 7
- 25
- 3
Correct answer: 5
Distance = sqrt((4-1)^2 + (6-2)^2) = sqrt(9+16) = sqrt(25) = 5.
Question 2: What is the midpoint of the segment joining (-2, 3) and (4, 7)?
- (1, 5) (Correct answer)
- (2, 10)
- (3, 2)
- (1, 4)
Correct answer: (1, 5)
Midpoint = ((-2+4)/2, (3+7)/2) = (1, 5).
Question 3: What is the slope of the line through (0, 0) and (3, 9)?
- 3 (Correct answer)
- 1/3
- 9
- 6
Correct answer: 3
Slope = (9-0)/(3-0) = 3.
Question 4: A point is reflected across the x-axis. If it was (5, -2), where is it now?
- (5, 2) (Correct answer)
- (-5, -2)
- (-5, 2)
- (2, 5)
Correct answer: (5, 2)
Reflecting across the x-axis negates the y-coordinate: (5, 2).
Question 5: Which transformation preserves both size and shape but changes orientation?
- Reflection (Correct answer)
- Dilation
- Stretch
- Shear
Correct answer: Reflection
A reflection is an isometry that reverses orientation while keeping size and shape.
Question 6: What is the equation of a line with slope 2 and y-intercept -3?
- y = 2x - 3 (Correct answer)
- y = -3x + 2
- y = 2x + 3
- y = 3x - 2
Correct answer: y = 2x - 3
Slope-intercept form y = mx + b gives y = 2x - 3.
Question 7: After translating (3, 4) by the vector (−2, 5), what is the image?
- (1, 9) (Correct answer)
- (5, -1)
- (1, -1)
- (-2, 20)
Correct answer: (1, 9)
Add the vector: (3-2, 4+5) = (1, 9).
Geometry Coordinate Geometry & Transformations 2
What is the distance between points (1, 2) and (4, 6)?