Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin.(1 point)
Responses
A. A′ (5, 10) and B′ (−10, −5)
B. A′ (5, 10) and B′ (10, 5)
C. A′ (1, 2) and B′ (−10, −5)
D. A′ (5, 10) and B′ (−2, −1)
To find the coordinates of A' and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin, you multiply the x and y coordinates of each point by the scale factor.
For point A (1, 2):
x-coordinate: 1 * 5 = 5
y-coordinate: 2 * 5 = 10
So the coordinates of A' are (5, 10).
For point B (-2, -1):
x-coordinate: -2 * 5 = -10
y-coordinate: -1 * 5 = -5
So the coordinates of B' are (-10, -5).
Therefore, the correct answer is A. A' (5, 10) and B' (-10, -5).