Question

Find the dilation of
4
4 with center
(
0
,

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

(
−
7
,

0
)
A (−7, 0)
𝐵

(
−
4
,

8
)
B (−4, 8)

Answer 1

To find the dilation of the points \(A(-7, 0)\) and \(B(-4, 8)\) with a center at the origin \((0, 0)\) and a dilation factor of \(4\), we can use the formula for dilation:

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

where \(P\) is the original point \((x, y)\), \(P'\) is the dilated point, and \(k\) is the dilation factor.

### For point \(A(-7, 0)\):

Here, \(x = -7\), \(y = 0\), and \(k = 4\).

\[
A' = (4 \cdot -7, 4 \cdot 0) = (-28, 0)
\]

### For point \(B(-4, 8)\):

Now, \(x = -4\), \(y = 8\), and \(k = 4\).

\[
B' = (4 \cdot -4, 4 \cdot 8) = (-16, 32)
\]

### Summary of Dilated Points:

- The dilation of point \(A(-7, 0)\) is \(A'(-28, 0)\).
- The dilation of point \(B(-4, 8)\) is \(B'(-16, 32)\).