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 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 can use the following formulas:
For point A:
A' = (x, y)
x = 7 * 2 = 14
y = 7 * 1 = 7
So, A' = (14, 7)
For point B:
B' = (x, y)
x = 7 * 4 = 28
y = 7 * 3 = 21
So, B' = (28, 21)
For point C:
C' = (x, y)
x = 7 * (-2) = -14
y = 7 * 5 = 35
So, C' = (-14, 35)
Therefore, the coordinates of A', B', and C' are A'(14, 7), B'(28, 21), and C'(-14, 35), respectively.