Question

Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13 , centered at the origin where the endpoints are A(−6,3) and B(−12,9) .(1 point) what were the original end points?

Answer 1

To find the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13, centered at the origin, we will apply the dilation formula for each endpoint.

The formula for dilation centered at the origin with a scale factor \( k \) is given by:
\[
(x', y') = (kx, ky)
\]

### Original Endpoints
The original endpoints are:
- \( A(-6, 3) \)
- \( B(-12, 9) \)

### Dilation by a Scale Factor of 13
1. For point A:
\[
A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39)
\]

2. For point B:
\[
B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117)
\]

### Result
The coordinates after dilation are:
- \( A'(-78, 39) \)
- \( B'(-156, 117) \)

So the original endpoints are \( A(-6, 3) \) and \( B(-12, 9) \), and the dilated endpoints are \( A'(-78, 39) \) and \( B'(-156, 117) \).