Line AB

Question

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)

A′ (1, 2)
and B′ (−10, −5)

A′ (5, 10)
and B′ (−10, −5)

A′ (5, 10)
and B′ (10, 5)

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 5 centered at the origin, we can use the following formula for dilation:

\[ (x, y) \rightarrow (kx, ky) \]

where \( k \) is the scale factor.

1. For point A(1, 2): \[ A' = (5 \times 1, 5 \times 2) = (5, 10) \]

2. For point B(-2, -1): \[ B' = (5 \times -2, 5 \times -1) = (-10, -5) \]

Therefore, the coordinates after dilation are:

A' (5, 10) and B' (-10, -5).

The correct response is:

A′ (5, 10) and B′ (−10, −5).