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).
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).
To find the coordinates of A', B', and C' after a dilation at the origin, we need to multiply the coordinates of each point by the scale factor.
Let the scale factor be represented by k.
The coordinates of A (2,1) after dilation can be found by multiplying each coordinate by k:
A' = (k * 2, k * 1) = (2k, k)
Similarly, the coordinates of B (4,3) after dilation can be found by multiplying each coordinate by k:
B' = (k * 4, k * 3) = (4k, 3k)
Finally, the coordinates of C (-2,5) after dilation can be found by multiplying each coordinate by k:
C' = (k * -2, k * 5) = (-2k, 5k)
Therefore, the coordinates of A' are (2k, k), the coordinates of B' are (4k, 3k), and the coordinates of C' are (-2k, 5k).