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′ (−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 negative 2 comma 6 right parenthesis
A′ (−8, 2) and B′ (2, −6)
None of the given choices for the coordinates of A' and B' are correct.
To find the coordinates of A' and B', we need to multiply each coordinate of A and B by the scale factor of 2.
For point A (-4, 1), when multiplied by 2, the coordinates become (2*-4, 2*1) = (-8, 2).
For point B (-1, 3), when multiplied by 2, the coordinates become (2*-1, 2*3) = (-2, 6).
Therefore, the correct coordinates for A' and B' are A' (-8, 2) and B' (-2, 6).