VITEEE 2021 Paper

One vertex of square is (−4,5) and equation of one diagonal is 7x−y+8=0
Diagonal of a square are perpendicular and bisect each other
Let the equation of the other diagonal be y=mx +c where m is the slope of the line and c is the y− intercept.
Since this line passes through (−4,5)
∴ 5=−4m+c... (i)
Since this line is at right angle to the line 7x−y+8=0 or y=7x+8, having slope =7,
∴ 7×m=−1 or m=

−1

7

Putting this value of m in equation (i) we get
5=−4×(

−1

7

)+c
or 5=

4

7

+c or c=5−

4

7

=

31

7

Hence equation of the other diagonal is
y=−

1

7

x+

31

7

or 7y=−x+31
or x+7y−31=0 or x+7y=31.