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)
Responses

A′(−18,9)
and B′(−36,27)
upper A prime left parenthesis negative 18 comma 9 right parenthesis and upper B prime left parenthesis negative 36 comma 27 right parenthesis

A′(−2,1)
and B′(−4,3)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(−2,1)
and B′(−12,9)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 right parenthesis

A′(−6,3)
and B′(−4,3)

Answer 1

To find the new coordinates A' and B' after dilating the line segment AB with a scale factor of 13 centered at the origin, we need to multiply each coordinate of points A and B by the scale factor.

Given:
- A(−6, 3)
- B(−12, 9)

### Calculate the coordinates:

1. **Dilation of A(−6, 3)**:
\[
A' = (−6 \times 13, 3 \times 13) = (−78, 39)
\]

2. **Dilation of B(−12, 9)**:
\[
B' = (−12 \times 13, 9 \times 13) = (−156, 117)
\]

It seems that there aren't any of the response options accurately reflecting the coordinates after dilation by a factor of 13.

To double-check:
\[
A' = (−6 \times 13, 3 \times 13) = (−78, 39)
\]
\[
B' = (−12 \times 13, 9 \times 13) = (−156, 117)
\]

None of the provided options match this dilation result, indicating either an issue with the question or the provided answers. If the intended scale factor and points are confirmed, the calculated coordinates are correct.