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)

Question

A′= (
)
B′= (
)
C′= (
)

Answer 1

To find the coordinates of a point after a dilation, we multiply the coordinates of the original point by the scale factor.

For point A(2,1), after a dilation with a scale factor of 7, we have:
A' = (7*2, 7*1) = (14, 7)

For point B(4,3), after a dilation with a scale factor of 7, we have:
B' = (7*4, 7*3) = (28, 21)

For point C(-2,5), after a dilation with a scale factor of 7, we have:
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)