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′ (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′ (−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′ (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′ (−2, −1)
None of the given options are correct.
To find the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:
A' = (5 * x, 5 * y)
B' = (5 * x, 5 * y)
So in this case, we would have:
A' = (5 * 1, 5 * 2) = (5, 10)
B' = (5 * -2, 5 * -1) = (-10, -5)
Therefore, the correct coordinates for A' and B' are:
A' (5, 10) and B' (-10, -5)