To find the coordinates of points \( A' \) and \( B' \) after a dilation centered at the origin with a scale factor of 12, we can use the following formula for dilation:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \( (x, y) \) are the original coordinates of the point, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the scale factor.
Given:
- Point \( A(-6, 4) \)
- Point \( B(-8, 2) \)
- Scale factor \( k = 12 \)
Let's calculate the new coordinates:
- For point \( A(-6, 4) \):
\[ A' = (12 \cdot -6, 12 \cdot 4) = (-72, 48) \]
- For point \( B(-8, 2) \):
\[ B' = (12 \cdot -8, 12 \cdot 2) = (-96, 24) \]
Therefore, the coordinates after dilation are:
- \( A'(-72, 48) \)
- \( B'(-96, 24) \)