Question

Select the coordinates A′
𝐴
′
and B′
𝐵
′
after dilation of the line segment AB
𝐴
𝐵
with a scale factor of 2, centered at the origin where the endpoints are A(3,7)
𝐴
(
3
,
7
)
and B(4,9)
𝐵
(
4
,
9
)
.(1 point)
Responses

A′(6,14)

Answer 1

To find the coordinates of the points A' and B' after dilation with a scale factor of 2, centered at the origin, you can use the following formula for dilation:

\[
(x', y') = (kx, ky)
\]

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

Given:
- Point A has coordinates \( A(3, 7) \)
- Point B has coordinates \( B(4, 9) \)
- Scale factor \( k = 2 \)

Now, applying the dilation to each point:

1. For point A:
\[
A' = (2 \cdot 3, 2 \cdot 7) = (6, 14)
\]

2. For point B:
\[
B' = (2 \cdot 4, 2 \cdot 9) = (8, 18)
\]

So, the coordinates after dilation are:
- \( A' = (6, 14) \)
- \( B' = (8, 18) \)

Therefore, the final answer is:
- **A′(6, 14)**
- **B′(8, 18)**