To reflect triangle ABC across the x-axis and the y-axis, we will follow these steps for each vertex:
- Reflect across the x-axis: For a point \((x, y)\), the reflection across the x-axis is \((x, -y)\).
- 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):
- Reflect across the x-axis: \[ A' = (2, -(-1)) = (2, 1) \]
- Reflect across the y-axis: \[ A'' = (-2, 1) \]
Vertex B = (6, -3):
- Reflect across the x-axis: \[ B' = (6, -(-3)) = (6, 3) \]
- Reflect across the y-axis: \[ B'' = (-6, 3) \]
Vertex C = (1, -3):
- Reflect across the x-axis: \[ C' = (1, -(-3)) = (1, 3) \]
- 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:
- \(A' = (-2, 1)\)
- \(B' = (-6, 3)\)
- \(C' = (-1, 3)\)