To find the dilation of a point from a center with a given scale factor, you use the formula:
\[ P' = (kx, ky) \]
where \( P \) is the original point, \( (x, y) \) are the coordinates of the point, \( k \) is the dilation factor, and \( P' \) is the new point after dilation.
Here, the dilation factor \( k \) is \( 5 \), and the center of dilation is \( (0, 0) \).
Let's find the dilation of points \( A(-7, -9) \) and \( B(6, -1) \).
For Point A (-7, -9):
\[ A' = (5 \cdot -7, 5 \cdot -9) = (-35, -45) \]
For Point B (6, -1):
\[ B' = (5 \cdot 6, 5 \cdot -1) = (30, -5) \]
Results:
- The dilation of point \( A(-7, -9) \) is \( A'(-35, -45) \).
- The dilation of point \( B(6, -1) \) is \( B'(30, -5) \).