Question

Line segment AB
A
B
has endpoints A (−6, 4)
A

(
−
6
,

4
)
and B (−8, 2)
B

(
−
8
,

2
)
. Find the coordinates of A′
A
′
and B′
B
′
after a dilation with a scale factor of 12
1
2
, centered at the origin.

Answer 1

To perform a dilation on a point with a scale factor \( k \) centered at the origin, you multiply the coordinates of the point by the scale factor.

Given the scale factor \( k = \frac{1}{2} \), we will find the coordinates of \( A' \) and \( B' \):

1. **For point A (-6, 4)**:
\[
A' = \left(-6 \times \frac{1}{2}, 4 \times \frac{1}{2}\right) = \left(-3, 2\right)
\]

2. **For point B (-8, 2)**:
\[
B' = \left(-8 \times \frac{1}{2}, 2 \times \frac{1}{2}\right) = \left(-4, 1\right)
\]

Thus, the coordinates after the dilation are:
- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)