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.(1 point)
A′
𝐴
′

() B′
𝐵
′

Answer 1

To find the coordinates of the points A' and B' after a dilation with a scale factor of \(\frac{1}{2}\) centered at the origin, we use the formula for dilation:

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

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

1. **For point A (-6, 4):**

Using the scale factor \( k = \frac{1}{2} \):

\[
A' = \left(\frac{1}{2} \cdot -6, \frac{1}{2} \cdot 4\right) = \left(-3, 2\right)
\]

2. **For point B (-8, 2):**

Using the same scale factor \( k = \frac{1}{2} \):

\[
B' = \left(\frac{1}{2} \cdot -8, \frac{1}{2} \cdot 2\right) = \left(-4, 1\right)
\]

Therefore, the coordinates after the dilation are:

- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)

Final results:
- \( A' = (-3, 2) \)
- \( B' = (-4, 1) \)