Question

Reflect triangle ABC
with respect to the x
-axis and the y
-axis. What are the vertices of triangle A′B′C′
A= (2, -1) B= (6, -3) C= (1, -3)

Answer 1

To reflect triangle ABC across the x-axis and the y-axis, we will follow these steps for each vertex:

1. Reflect across the x-axis: For a point \((x, y)\), the reflection across the x-axis is \((x, -y)\).
2. Reflect across the y-axis: For a point \((x, y)\), the reflection across the y-axis is \((-x, y)\).

For each vertex of triangle ABC, let's perform these reflections:

### Vertex A = (2, -1):
1. Reflect across the x-axis:
\[
A' = (2, -(-1)) = (2, 1)
\]
2. Reflect across the y-axis:
\[
A'' = (-2, 1)
\]

### Vertex B = (6, -3):
1. Reflect across the x-axis:
\[
B' = (6, -(-3)) = (6, 3)
\]
2. Reflect across the y-axis:
\[
B'' = (-6, 3)
\]

### Vertex C = (1, -3):
1. Reflect across the x-axis:
\[
C' = (1, -(-3)) = (1, 3)
\]
2. Reflect across the y-axis:
\[
C'' = (-1, 3)
\]

### Final Vertices after Reflection:
After reflecting the triangle ABC across both axes, we get the vertices of triangle A'B'C' as follows:
- \(A'' = (-2, 1)\)
- \(B'' = (-6, 3)\)
- \(C'' = (-1, 3)\)

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