To find the coordinates of the points \( A' \) and \( B' \) after a dilation with a scale factor of 12 centered at the origin, we can use the formula for dilation. If a point \( (x, y) \) is dilated with a scale factor \( k \), the new coordinates \( (x', y') \) are given by:
\[ (x', y') = (k \cdot x, k \cdot y) \]
Here, \( k = 12 \).
Step 1: Find \( A' \)
The coordinates of point \( A \) are \( (-6, 4) \).
Using the dilation formula:
\[ A' = (12 \cdot -6, 12 \cdot 4) \] \[ A' = (-72, 48) \]
Step 2: Find \( B' \)
The coordinates of point \( B \) are \( (-8, 2) \).
Using the dilation formula:
\[ B' = (12 \cdot -8, 12 \cdot 2) \] \[ B' = (-96, 24) \]
Conclusion
The coordinates of the dilated points are:
- \( A' = (-72, 48) \)
- \( B' = (-96, 24) \)