Question

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)

Answer 1

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:

$$(x^{\prime },y^{\prime })=(kx,ky)$$

where $k$ is the scale factor.

For point A(1, 2): $$A^{\prime }=(5\cdot 1,5\cdot 2)=(5,10)$$

For point B(−2, −1): $$B^{\prime }=(5\cdot -2,5\cdot -1)=(-10,-5)$$

Therefore, the coordinates after the dilation are:

• A' = (5, 10)
• B' = (-10, -5)

The correct response is: A′ (5, 10) and B′ (−10, −5).