Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.(1 point)
Responses
A. A′ (−5, −2) and B′ (−2, 6)
B. A′ (8, −2) and B′ (2, −6)
C. A′ (−8, 2) and B′ (2, −6)
D. A′ (−8, 2) and B′ (−2, 6)
To find the coordinates after a dilation with a scale factor of 2 and a center point of dilation at the origin, we will multiply the x and y coordinates of each point by 2.
Point A (−4, 1) becomes A' (2*(-4), 2*1) = (-8, 2).
Point B (−1, 3) becomes B' (2*(-1), 2*3) = (-2, 6).
Therefore, the coordinates of A′ and B′ after the dilation are A' (−8, 2) and B' (−2, 6).
The correct answer is D. A′ (−8, 2) and B′ (−2, 6).