To find the coordinates of points A' and B' after a dilation with a scale factor of 4 and center of dilation at the origin (0, 0), we apply the dilation formula:
\[ A' = (k \cdot x, k \cdot y) \] \[ B' = (k \cdot x, k \cdot y) \]
where \( k \) is the scale factor, and \( (x, y) \) are the coordinates of the original points.
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For point A (2, -5): \[ A' = (4 \cdot 2, 4 \cdot -5) = (8, -20) \]
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For point B (-3, -2): \[ B' = (4 \cdot -3, 4 \cdot -2) = (-12, -8) \]
So, the coordinates after dilation are:
- A' = (8, -20)
- B' = (-12, -8)
Thus, the correct response is: A′ (8, −20) and B′ (−12, −8)