To translate the vertices of triangle \(ABC\) by the transformation \(T(-3, -5)\), you need to subtract 3 from the x-coordinates and 5 from the y-coordinates of each vertex.
The original vertices of triangle \(ABC\) are:
- \(A(4, -2)\)
- \(B(-1, -3)\)
- \(C(2, 1)\)
Let's apply the translation to each vertex:
-
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 \(C(2, 1)\): \[ C' = (2 - 3, 1 - 5) = (-1, -4) \]
Now, let's summarize the vertices of triangle \(A'B'C'\):
- \(A' = (1, -7)\)
- \(B' = (-4, -8)\)
- \(C' = (-1, -4)\)
Thus, the vertices of triangle \(A'B'C'\) are:
- \(A' (1, -7)\)
- \(B' (-4, -8)\)
- \(C' (-1, -4)\)
In conclusion:
- \(A' = (1, -7)\)
- \(B' = (-4, -8)\)
- \(C' = (-1, -4)\)