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 with a scale factor of 7 and a center point of dilation at the origin (0,0) .
To find the coordinates of each vertex after the dilation, we multiply the x- and y-coordinates of each vertex by the scale factor.
For vertex A(2,1), the coordinates after dilation are:
x-coordinate: 2 * 7 = 14
y-coordinate: 1 * 7 = 7
Therefore, A' = (14, 7).
For vertex B(4,3), the coordinates after dilation are:
x-coordinate: 4 * 7 = 28
y-coordinate: 3 * 7 = 21
Therefore, B' = (28, 21).
For vertex C(-2,5), the coordinates after dilation are:
x-coordinate: -2 * 7 = -14
y-coordinate: 5 * 7 = 35
Therefore, C' = (-14, 35).
So, the coordinates of A', B', and C' after the dilation are:
A' = (14, 7)
B' = (28, 21)
C' = (-14, 35)