To find the dilated points \( A' \) and \( B' \) of the points \( A(-6, -5) \) and \( B(-3, 5) \) with a dilation factor of \( 0.25 \) and centered at \( (0, 0) \), we can use the formula for dilation:
\[ A' = \left( k \cdot x, k \cdot y \right) \] where \( k \) is the dilation factor and \( (x, y) \) are the coordinates of the original point.
Dilation of Point A
For point \( A(-6, -5) \):
- \( x = -6 \)
- \( y = -5 \)
- \( k = 0.25 \)
Calculating the dilated coordinates:
\[ A' = \left( 0.25 \cdot (-6), 0.25 \cdot (-5) \right) = \left( -1.5, -1.25 \right) \]
Dilation of Point B
For point \( B(-3, 5) \):
- \( x = -3 \)
- \( y = 5 \)
- \( k = 0.25 \)
Calculating the dilated coordinates:
\[ B' = \left( 0.25 \cdot (-3), 0.25 \cdot 5 \right) = \left( -0.75, 1.25 \right) \]
Final Results
Thus, the dilated points are:
\[ A' = (-1.5, -1.25) \] \[ B' = (-0.75, 1.25) \]