Question

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

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation centered at the origin with a scale factor of 2, we use the formula for dilation:

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

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

Given the scale factor \( k = 2 \):

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

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

Thus, the coordinates after dilation are:

- \( A' = (6, 14) \)
- \( B' = (8, 18) \)