Question

Reflect triangle ABC with respect to the 2-axis and the y-axis. What are the vertices of triangle A' * B' C^ prime prime

(1 point)

The vertices of triangle A' * B' * C' are A' * (2, 1) B (6,3), and C' (1, 3).

The vertices of triangle A' * B' * C' are A' * (- 2, 1) B' * (- 6, 3) and C' * (- 1, 3)

The vertices of triangle A' * B' * C' are A' * (- 2, 1) B' * (- 1, 3) and C' * (- 6, 3)

The vertices of triangle A' * B' * C' are A' * (- 2, - 1) B' * (- 6, - 3) and C' * (- 1, - 3)

Answer 1

To reflect triangle ABC with vertices \( A(2, 1) \), \( B(6, 3) \), and \( C(1, 3) \) first across the x-axis and then across the y-axis, we follow these steps:

1. **Reflect across the x-axis**:
- For point \( A(2, 1) \):
\[
A'(2, -1)
\]
- For point \( B(6, 3) \):
\[
B'(6, -3)
\]
- For point \( C(1, 3) \):
\[
C'(1, -3)
\]

After reflection across the x-axis, the points are:
- \( A'(2, -1) \)
- \( B'(6, -3) \)
- \( C'(1, -3) \)

2. **Reflect across the y-axis**:
- For point \( A'(2, -1) \):
\[
A''(-2, -1)
\]
- For point \( B'(6, -3) \):
\[
B''(-6, -3)
\]
- For point \( C'(1, -3) \):
\[
C''(-1, -3)
\]

After reflection across the y-axis, the final vertices are:
- \( A''(-2, -1) \)
- \( B''(-6, -3) \)
- \( C''(-1, -3) \)

Thus, the vertices of triangle \( A'' B'' C'' \) are \( A''(-2, -1) \), \( B''(-6, -3) \), and \( C''(-1, -3) \).

So the correct description of the vertices is:
- The vertices of triangle \( A' B' C' \) are \( A' (-2, -1) \), \( B' (-6, -3) \), and \( C' (-1, -3) \).