To find the coordinates of points A' and B' after a dilation with a scale factor of 2 with the center of dilation at the origin (0, 0), we can use the following formula for dilation:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the scale factor.
For point A(−4, 1):
- The coordinates after dilation will be: \[ A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2) \]
For point B(−1, 3):
- The coordinates after dilation will be: \[ B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6) \]
Therefore, after the dilation, the coordinates of points A' and B' are:
A′ (−8, 2) and B′ (−2, 6).
So the correct response is:
A′ (−8, 2) and B′ (−2, 6).