To find the coordinates of points \( A' \) and \( B' \) after a dilation centered at the origin with a scale factor of \( k = 12 \), we can use the formula for dilation:
\[ A' = (kx_A, ky_A) \] \[ B' = (kx_B, ky_B) \]
where \( (x_A, y_A) \) and \( (x_B, y_B) \) are the coordinates of points \( A \) and \( B \), respectively.
Given the coordinates of \( A \) are \( (-6, 4) \) and the coordinates of \( B \) are \( (-8, 2) \):
For point A:
\[ A' = (12 \cdot -6, 12 \cdot 4) \] \[ A' = (-72, 48) \]
For point B:
\[ B' = (12 \cdot -8, 12 \cdot 2) \] \[ B' = (-96, 24) \]
Thus, the coordinates after the dilation are:
\[ A' (-72, 48) \quad B' (-96, 24) \]
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