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 \(B'(-16, 32)\).