1. Identify the relationship between diagonals
In a square, the two diagonals are always perpendicular to each other.
Given diagonal: 7x−y+8=0
2. Find the slope of the given diagonal
The equation is in the form Ax+By+C=0.
The slope (m1) is given by −BA:
3. Find the slope of the required diagonal
Since the diagonals are perpendicular, the product of their slopes is −1 (m1×m2=−1).
4. Check the vertex
The vertex (−4,5) does not satisfy the given diagonal equation:
7(−4)−(5)+8=−28−5+8=−25=0
This means the vertex (−4,5) must lie on the other diagonal (the one we need to find).
5. Form the equation of the second diagonal
Using the point-slope form y−y1=m(x−x1) with point (−4,5) and slope m=−71:
Conclusion:
The equation of the other diagonal is x+7y=31.
Correct Option: (b) or (c) x+7y=31
