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′ (−8, 2) and B′ (−2, 6) upper a prime left parenthesis negative 8 comma 2 right parenthesis and upper b prime left parenthesis negative 2 comma 6 right parenthesis A′ (−5, −2) and B′ (−2, 6) upper A prime left parenthesis negative 5 comma negative 2 right parenthesis and upper B prime left parenthesis negative 2 comma 6 right parenthesis A′ (8, −2) and B′ (2, −6) upper A prime left parenthesis 8 comma negative 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis A′ (−8, 2) and B′ (2, −6) upper A prime left parenthesis negative 8 comma 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis
To find the coordinates of A' after a dilation with a scale factor of 2 and a center point of dilation at the origin, we can multiply the x-coordinate and the y-coordinate of A by the scale factor.
The x-coordinate of A' is: (-4) * 2 = -8
The y-coordinate of A' is: 1 * 2 = 2
Therefore, A' has the coordinates (-8, 2).
Similarly, the x-coordinate of B' is: (-1) * 2 = -2
The y-coordinate of B' is: 3 * 2 = 6
Therefore, B' has the coordinates (-2, 6).
So, the correct answer is:
A' (-8, 2) and B' (-2, 6)