Question

The vertices of triangle symbol ABC△ABC are Aleft parenthesis 4 comma negative 2 right parenthesis(4,−2)​, Bleft parenthesis negative 1 comma negative 3 right parenthesis(−1,−3)​, and Cleft parenthesis 2 comma 1 right parenthesis(2,1). For the translation​ below, give the vertices of triangle symbol Upper A prime Upper B prime Upper C prime△A′B′C′.
Upper T Subscript left angle negative 3 comma negative 5 right angle Baseline left parenthesis triangle symbol ABC right parenthesisT−3,−5(△ABC)
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Part 1
The vertices of triangle symbol Upper A prime Upper B prime Upper C prime△A′B′C′ are Upper A primeA′enter your response here​, Upper B primeB′enter your response here​, and Upper C primeC′enter your response here.
​(Simplify your answers. Type ordered​ pairs.)

Answer 1

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:

1. For vertex \(A(4, -2)\):
\[
A' = (4 - 3, -2 - 5) = (1, -7)
\]

2. For vertex \(B(-1, -3)\):
\[
B' = (-1 - 3, -3 - 5) = (-4, -8)
\]

3. 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:

- \(A' = (1, -7)\)
- \(B' = (-4, -8)\)
- \(C' = (-1, -4)\)