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 multiply each coordinate by the scale factor.
Coordinates of A':
A' = (7 * x-coordinate of A, 7 * y-coordinate of A)
= (7 * 2, 7 * 1)
= (14, 7)
Coordinates of B':
B' = (7 * x-coordinate of B, 7 * y-coordinate of B)
= (7 * 4, 7 * 3)
= (28, 21)
Coordinates of C':
C' = (7 * x-coordinate of C, 7 * y-coordinate of C)
= (7 * -2, 7 * 5)
= (-14, 35)
Therefore, the coordinates of A', B', and C' are:
A' = (14, 7)
B' = (28, 21)
C' = (-14, 35)