Question

Find the dilation of
4
4 with center
(
0
,

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

(
−
2
,

4
)
A (−2, 4)
𝐵

(
7
,

−
7
)
B (7, −7)



𝐴
′
A
′

(
(

)
)



𝐵
′
B
′

(
(

)
)

Answer 1

To find the dilation of points \(A(-2, 4)\) and \(B(7, -7)\) with a center at the origin \((0, 0)\) and a dilation factor of \(k = 4\), we can apply the dilation formula:

\[
A' = (kx, ky)
\]

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

### For point \(A(-2, 4)\):

1. Calculate the dilated coordinates:
\[
A' = (4 \cdot -2, 4 \cdot 4) = (-8, 16)
\]

### For point \(B(7, -7)\):

1. Calculate the dilated coordinates:
\[
B' = (4 \cdot 7, 4 \cdot -7) = (28, -28)
\]

### Summary of dilated points:
- The dilated point \(A'\) is \((-8, 16)\).
- The dilated point \(B'\) is \((28, -28)\).

Therefore:
\[
A'(-8, 16)
\]
\[
B'(28, -28)
\]