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′ (5, 10) and B′ (10, 5) upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis 10 comma 5 right parenthesis A′ (5, 10) and B′ (−10, −5) upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis A′ (1, 2) and B′ (−10, −5) upper A prime left parenthesis 1 comma 2 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis A′ (5, 10) and B′ (−2, −1)

Question

GPT-4o mini · Answer

To perform a dilation with a scale factor of 5 centered at the origin, we multiply the coordinates of each point by the scale factor.

For point A(1, 2):

A' = (1 * 5, 2 * 5) = (5, 10)

For point B(−2, −1):

B' = (−2 * 5, −1 * 5) = (−10, −5)

So, the coordinates after dilation are:

A' = (5, 10)
B' = (−10, −5)

The correct response is: A′ (5, 10) and B′ (−10, −5).