Find the dilation of

Question

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