Triangle ABC has vertices point A (−3,−3) , point B (5,−3) , and point C (2, 4) . Find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 2 and a center point of dilation at the origin.
To find the coordinates of A', B', and C' after dilation with a scale factor of 2 and a center point of dilation at the origin, we can use the formula:
(x', y') = (kx, ky), where (x', y') are the new coordinates after dilation, (x, y) are the original coordinates, and k is the scale factor.
For point A: (x, y) = (-3, -3)
(x', y') = (2 * -3, 2 * -3)
(x', y') = (-6, -6)
For point B: (x, y) = (5, -3)
(x', y') = (2 * 5, 2 * -3)
(x', y') = (10, -6)
For point C: (x, y) = (2, 4)
(x', y') = (2 * 2, 2 * 4)
(x', y') = (4, 8)
So, the coordinates of A' are (-6, -6), the coordinates of B' are (10, -6), and the coordinates of C' are (4, 8).