Question 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′ (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 10 comma 5 right parenthesis A′ (5, 10) and B′ (−10, −5)
1 answer
To determine the coordinates of points A' and B' after a dilation with a scale factor of 5 about the origin, we use the formula for dilation:
\[ (x', y') = (kx, ky) \]
where \(k\) is the scale factor.
For point A(1, 2): \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]
For point B(−2, −1): \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]
Therefore, the coordinates after the dilation are:
The correct response is: A′ (5, 10) and B′ (−10, −5).
