The vertices's of triangle ABC are A(-1,2), b(0,3), and c(3,1). Determine the vertices A', B', and C' of the image of triangle ABC after a reflection across the x-axis.
All the x values are the same and the y values change sign so for example
(-1,2)---> (-1,-2)
To determine the vertices A', B', and C' of the image of triangle ABC after a reflection across the x-axis, we need to change the sign of the y-coordinates of the original vertices.
Let's go through the process step by step:
1. Original coordinates of the vertices:
- A(-1, 2)
- B(0, 3)
- C(3, 1)
2. Reflection across the x-axis:
- For each vertex, we need to change the sign of the y-coordinate while keeping the x-coordinate the same.
- A' will have the same x-coordinate as A, but the y-coordinate will be -2.
- B' will have the same x-coordinate as B, but the y-coordinate will be -3.
- C' will have the same x-coordinate as C, but the y-coordinate will be -1.
3. Final coordinates of the vertices:
- A'(-1, -2)
- B'(0, -3)
- C'(3, -1)
Therefore, the vertices A', B', and C' of the image of triangle ABC after a reflection across the x-axis are A'(-1, -2), B'(0, -3), and C'(3, -1).