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′left parenthesis 1 comma negative 7 right parenthesis(1,−7)​, Upper B primeB′enter your response here​, and Upper C primeC′enter your response here.

Answer 1

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:

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 \( C(2, 1) \):
\[
C' = (2 - 3, 1 - 5) = (-1, -4)
\]

Thus, the vertices of triangle \( A'B'C' \) are:
- \( A'(1, -7) \)
- \( B'(-4, -8) \)
- \( C'(-1, -4) \)

So, the complete answer is:
- \( A' = (1, -7) \)
- \( B' = (-4, -8) \)
- \( C' = (-1, -4) \)