To find the coordinates of points A and B after a dilation with a scale factor of 2, centered at the origin, we apply the dilation transformation to each coordinate.
The dilation transformation can be calculated using the formula:
\[ (x', y') = (kx, ky) \]
where \(k\) is the scale factor, and \((x, y)\) are the original coordinates.
Given:
- \(A(3, 7)\)
- \(B(4, 9)\)
- Scale factor \(k = 2\)
Let's calculate the new coordinates for point A:
\[ A' = (2 \cdot 3, 2 \cdot 7) = (6, 14) \]
Now for point B:
\[ B' = (2 \cdot 4, 2 \cdot 9) = (8, 18) \]
So after dilation, the coordinates are:
- \(A'(6, 14)\)
- \(B'(8, 18)\)
Therefore, the correct response is: A′(6,14) and B′(8,18)