To find the coordinates of points A' and B' after a dilation with a scale factor of 2 centered at the origin, we use the dilation formula:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \(k\) is the scale factor and \((x, y)\) are the original coordinates of the points.
Given:
- Point A at \((-4, 1)\)
- Point B at \((-1, 3)\)
Now, applying the dilation with a scale factor of 2:
For point A: \[ A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2) \]
For point B: \[ B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6) \]
Thus, the coordinates after dilation are:
- \(A' = (-8, 2)\)
- \(B' = (-2, 6)\)
So, the correct answer is: A′ (−8, 2) and B′ (−2, 6)