To find the dilation of points \(A(-7, -9)\) and \(B(6, -1)\) with center at \((0, 0)\) and a dilation factor \(k\), we use the formula for dilation which is given by:
\[ D_k(x, y) = (kx, ky) \]
This means that each coordinate of the point is multiplied by the dilation factor \(k\).
For Point A (-7, -9):
- The dilation of point \(A\) can be calculated as follows: \[ A' = D_k(-7, -9) = (k \cdot -7, k \cdot -9) = (-7k, -9k) \]
For Point B (6, -1):
- Similarly, the dilation of point \(B\) is: \[ B' = D_k(6, -1) = (k \cdot 6, k \cdot -1) = (6k, -1k) = (6k, -k) \]
Summary:
- The dilated point \(A'\) is \((-7k, -9k)\)
- The dilated point \(B'\) is \((6k, -k)\)
If you have a specific dilation factor \(k\), you can substitute that value into these equations to find the coordinates of the dilated points.