To perform the translation \( T_{-3, -5} \) on the triangle \( ABC \), we subtract 3 from the x-coordinates and 5 from the y-coordinates of each vertex.
Given the vertices of triangle \( ABC \):
- \( A(4, -2) \)
- \( B(-1, -3) \)
- \( C(2, 1) \)
We will apply the translation:
-
For vertex \( A(4, -2) \): \[ A' = (4 - 3, -2 - 5) = (1, -7) \]
-
For vertex \( B(-1, -3) \): \[ B' = (-1 - 3, -3 - 5) = (-4, -8) \]
-
For vertex \( C(2, 1) \): \[ C' = (2 - 3, 1 - 5) = (-1, -4) \]
Thus, the vertices of triangle \( A'B'C' \) are:
- \( A'(1, -7) \)
- \( B'(-4, -8) \)
- \( C'(-1, -4) \)
So, the complete answer is:
- \( A' = (1, -7) \)
- \( B' = (-4, -8) \)
- \( C' = (-1, -4) \)