Triangle ABC has vertices point A (2,1), point B (4,3), and point C (-2,5). Find the coordinates of A', B', and C' after a dilation at the origin (0,0).

Answer 1

To find the coordinates of A', B', and C' after a dilation at the origin of scale factor k, multiply the coordinates of each point by k.

For point A (2,1), the dilation at the origin is kA(2,1) = (2k, k).

For point B (4,3), the dilation at the origin is kB(4,3) = (4k, 3k).

For point C (-2,5), the dilation at the origin is kC(-2,5) = (-2k, 5k).

Therefore, the coordinates of A', B', and C' after a dilation at the origin are:
A' = (2k, k),
B' = (4k, 3k),
C' = (-2k, 5k).