Question

Select the coordinates of A' and B' after dilation of the line segment AB with a scale factor of 4, centered at the origin where the endpoints are A(-2, -3) and B(-4, -5).(1 point)
Responses

A' (-2, 3) and B' (-4, -5)
A' (-2, 3) and B' (-4, -5)

A' (8, 12) and B' (16, 20)
A' (8, 12) and B' (16, 20)

A' (-8, -12) and B' (-4, -5)
A' (-8, -12) and B' (-4, -5)

A' (-8, -12) and B' (-16, -20)

Answer 1

To find the coordinates of points A' and B' after dilation with a scale factor of 4 centered at the origin, we can use the following formula:

Dilation formula: \( (x, y) \rightarrow (kx, ky) \)

where \( k \) is the scale factor and \( (x, y) \) are the original coordinates.

Given:
- Point A: \((-2, -3)\)
- Point B: \((-4, -5)\)
- Scale factor \( k = 4 \)

Now, we will apply the dilation to each point.

For point A:
\[
A' = (4 \times -2, 4 \times -3) = (-8, -12)
\]

For point B:
\[
B' = (4 \times -4, 4 \times -5) = (-16, -20)
\]

Thus, the coordinates of A' and B' after dilation are:
- A' (-8, -12)
- B' (-16, -20)

So the correct response is:
**A' (-8, -12) and B' (-16, -20)**.