Question
A dilation by a scale factor of 2 centered at (2,-1) is performed on triangle ABC.
A(-3,-1) B(1,2) C(2,-1)
What are the coordinates of A'B'C'
A(-3,-1) B(1,2) C(2,-1)
What are the coordinates of A'B'C'
Answers
GPT 3.5
To find the coordinates of A', B', and C', we can perform the dilation by multiplying the coordinates of each point by the scale factor of 2 and then translating the points to the center of dilation at (2, -1).
A' = (2 + 2(-3 - 2), -1 + 2(-1 - (-1))) = (2 - 10, -1) = (-8, -1)
B' = (2 + 2(1 - 2), -1 + 2(2 - (-1))) = (2 - 2, -1 + 6) = (0, 5)
C' = (2 + 2(2 - 2), -1 + 2(-1 - (-1))) = (2, -1)
Therefore, the coordinates of A'B'C' are A'(-8, -1), B'(0, 5), and C'(2, -1).
A' = (2 + 2(-3 - 2), -1 + 2(-1 - (-1))) = (2 - 10, -1) = (-8, -1)
B' = (2 + 2(1 - 2), -1 + 2(2 - (-1))) = (2 - 2, -1 + 6) = (0, 5)
C' = (2 + 2(2 - 2), -1 + 2(-1 - (-1))) = (2, -1)
Therefore, the coordinates of A'B'C' are A'(-8, -1), B'(0, 5), and C'(2, -1).