Given the vertices of triangle ABC:
A(2, 5), B(-3, 3), C(2, -1)
Let's dilate the triangle ABC by a scale factor of 2 with a center of dilation of (2, 3)
Here, since we have a scale factor, k, of 2 and center of dilation (2, 3), apply the formula:
(x', y') = k(x - a)+a, k(y - b)+ b
Where:
(a, b) is the center of dilation: (2, 3)
(x, y) is the coordinate
(x' y') is the new coordinate
k is the sale factor = 2
Thus, we have the following:
A(2, 5) ==> 2(2 - 2)+2, 2(5 - 3)+3 ==> 2(0)+2, 2(2)+3 ==> (2, 9)
B(-3, 3) ==> 2(-3 - 2)+2, 2(3 - 3)+3 ==> 2(-5)+2, 2(0)+3 ==> (-8, 3)
C(2, -1) ==> 2(2 - 2)+2, 2(-1 - 3)+3 ==> 2(0)+2, 2(-4)+3 ==> (2, -5)
Therefore, the vertices of triangle ABC after the dilation are:
A'(2, 9), B'(-8, 3), C'(2, -5)
ANSWER:
A'(2, 9), B'(-8, 3), C'(2, -5)