To find the coordinates of points A and B after a dilation with a scale factor of 2 and center of dilation at the origin, we can use the following formula for dilation:
\[ (x', y') = (kx, ky) \]
where \((x, y)\) are the original coordinates, \(k\) is the scale factor, and \((x', y')\) are the coordinates after dilation.
Given:
- Point A has coordinates \((-4, 1)\)
- Point B has coordinates \((-1, 3)\)
- Scale factor \(k = 2\)
Now we apply the formula:
-
For point A: \[ A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2) \]
-
For point B: \[ B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6) \]
After dilation, the coordinates are:
- A' is \((-8, 2)\)
- B' is \((-2, 6)\)
Thus, the dilated coordinates are:
- A' (-8, 2) and B' (-2, 6)
The correct choice is: A' (-8, 2) and B' (-2, 6).