NIMCET 2015 — Mathematics PYQ

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 ($m_1$) is given by $-\frac{A}{B}$:

3. Find the slope of the required diagonal

Since the diagonals are perpendicular, the product of their slopes is $-1$ ($m_1\times m_2=-1$).

4. Check the vertex

The vertex $(-4,5)$ does not satisfy the given diagonal equation:

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 $y-y_1=m(x-x_1)$ with point $(-4,5)$ and slope $m=-\frac{1}{7}$:

Conclusion:

The equation of the other diagonal is $x+7y=31$.

Correct Option: (b) or (c) $x+7y=31$