Respuesta :
To find the coordinates of the vertex B after reflecting triangle ABC across the line y=1, we can follow these steps:
1. **Find the line of reflection:**
- Since the line of reflection is y=1, the distance between the original point and the line of reflection is twice the distance between the reflected point and the line of reflection.
2. **Reflect point B across the line y=1:**
- The y-coordinate of point B will be the same after reflection across the line y=1, and the x-coordinate will be reflected across the line.
- Given the original coordinates of B as (-2,4), the reflected coordinates of B will have the same y-coordinate (4) and a new x-coordinate obtained by calculating the distance between the original x-coordinate (-2) and the line of reflection (y=1) and then reflecting it across the line.
Calculating the distance between point B and the line y=1:
- Distance = |y-coordinate of B - y-coordinate of the line of reflection| = |4 - 1| = 3
Reflecting the x-coordinate of B across the line y=1:
- The x-coordinate of the reflected point B will be 3 units away from the line of reflection in the opposite direction.
- So, the x-coordinate of the reflected point B will be (-2 - 2(3)) = -8.
Therefore, the coordinates of the vertex B after reflecting triangle ABC across the line y=1 will be (-8,4).
