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′ (−2, −1) upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 2 comma negative 1 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′ (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
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 need to multiply the x and y coordinates of A and B by the scale factor.
The coordinates of A are (1, 2).
To find the coordinates of A', we multiply each coordinate by 5:
x-coordinate of A' = 1 * 5 = 5
y-coordinate of A' = 2 * 5 = 10
Therefore, A' is (5, 10).
The coordinates of B are (-2, -1).
To find the coordinates of B', we multiply each coordinate by 5:
x-coordinate of B' = -2 * 5 = -10
y-coordinate of B' = -1 * 5 = -5
Therefore, B' is (-10, -5).
Thus, the correct answer is:
A' (5, 10) and B' (-10, -5)