Question

Find the dilation of
0.25
0.25 with center
(
0
,

0
)
(0, 0) for the following points if
𝐴

(
−
8
,

1
)
A (−8, 1)
𝐵

(
−
2
,

6
)
B (−2, 6)

Answer 1

To find the dilation of a point with center \((0, 0)\) and a factor of \(k = 0.25\), we use the dilation formula:

\[
D(k, (x, y)) = (k \cdot x, k \cdot y)
\]

Let's apply this to the given points \(A(-8, 1)\) and \(B(-2, 6)\).

1. **For Point A (-8, 1)**:
- Dilation of \(A\):
\[
D(0.25, A) = (0.25 \cdot (-8), 0.25 \cdot 1)
\]
\[
= (-2, 0.25)
\]

2. **For Point B (-2, 6)**:
- Dilation of \(B\):
\[
D(0.25, B) = (0.25 \cdot (-2), 0.25 \cdot 6)
\]
\[
= (-0.5, 1.5)
\]

Thus, the results of the dilations are:
- The dilation of point \(A(-8, 1)\) is \((-2, 0.25)\).
- The dilation of point \(B(-2, 6)\) is \((-0.5, 1.5)\).