Select the coordinates A′

Question

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)