Question

The vertices of triangle symbol ABC△ABC are Aleft parenthesis 4 comma negative 2 right parenthesis(4,−2)​, Bleft parenthesis negative 5 comma negative 1 right parenthesis(−5,−1)​, and Cleft parenthesis 5 comma 2 right parenthesis(5,2). 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 1 comma 6 right angle Baseline left parenthesis triangle symbol ABC right parenthesisT1,6(△ABC)
Question content area bottom
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 \( T_{1,6} \), we need to add \( 1 \) to the x-coordinates and \( 6 \) to the y-coordinates of each vertex.

Given the vertices:
- \( A(4, -2) \)
- \( B(-5, -1) \)
- \( C(5, 2) \)

We perform the translation as follows:

1. For vertex \( A \):
\[
A' = (4 + 1, -2 + 6) = (5, 4)
\]

2. For vertex \( B \):
\[
B' = (-5 + 1, -1 + 6) = (-4, 5)
\]

3. For vertex \( C \):
\[
C' = (5 + 1, 2 + 6) = (6, 8)
\]

So, the vertices of triangle \( A'B'C' \) after the translation \( T_{1,6} \) are:
- \( A' = (5, 4) \)
- \( B' = (-4, 5) \)
- \( C' = (6, 8) \)

Thus, we write:
**The vertices of triangle \( \triangle A'B'C' \) are \( A' (5, 4) \), \( B' (-4, 5) \), and \( C' (6, 8) \).**