Find the dilation of

Question

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 \((-0.5, 1.5)\).