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 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)
upper A prime left parenthesis negative 8 comma 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis
A′ (8, −2) and B′ (2, −6)
None of the given options are correct.
To 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, we can use the following formulas:
For a point (x, y) dilated with a scale factor of 2:
A' = (2x, 2y)
Using these formulas, the coordinates of A' and B' can be calculated as follows:
A' = (2*(-4), 2*1) = (-8, 2)
B' = (2*(-1), 2*3) = (-2, 6)
Therefore, the correct answer is:
A' (-8, 2) and B' (-2, 6)