In triangle `A B C` , the equation of the right bisectors of the sides `A B` and `A C` are `x+y=0` and `y-x=0` , respectively. If `A-=(5,7)` , then find the equation of side `B Cdot`

Explanation

To find the equation of side BC in triangle ABC, given the right bisectors of sides AB and AC, we can follow these steps:

### Step 1: Identify the coordinates of points B and C
We know that the right bisector of side AB is given by the equation \(x + y = 0\). This means that the midpoint of segment AB lies on this line. Since point A has coordinates \(A(5, 7)\), we can denote the coordinates of point B as \(B(5, y_1)\).

Similarly, the right bisector of side AC is given by the equation \(y - x = 0\), which means that the midpoint of segment AC lies on this line. We can denote the coordinates of point C as \(C(x_2, 7)\).

### Step 2: Find the coordinates of points B and C
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