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) .(2 points)
A′= (___)
B′= (___)
C′= (___)
To 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), we need to multiply the x and y coordinates of each point by the scale factor.
For point A(2,1):
x-coordinate of A' = 2 * 7 = 14
y-coordinate of A' = 1 * 7 = 7
So, A' = (14, 7).
For point B(4,3):
x-coordinate of B' = 4 * 7 = 28
y-coordinate of B' = 3 * 7 = 21
So, B' = (28, 21).
For point C(-2,5):
x-coordinate of C' = -2 * 7 = -14
y-coordinate of C' = 5 * 7 = 35
So, C' = (-14, 35).
Therefore, the coordinates of A', B', and C' are:
A' = (14, 7)
B' = (28, 21)
C' = (-14, 35)