UPSC NDA Math Model Paper 2

Given, 3x + 2y = 5 is the equation of one diagonal of the square.

Consider m1 be the slope of one diagonal. and m2 be the slope of other diagonal.
⇒2y=−3x+5
⇒y=

−3

2

x+

5

2

⇒m1=

−3

2

In square, the diagonals are perpendicular to each other.
⇒m1m2=−1
⇒m2=

2

3

Equation of other diagonal is
y=m2x+c
⇒y=

2

3

x+c .......(1)
Since, the other diagonal is passing through the point (1, -1). It must satisfy the equation of line.
Put y = -1 and x = 1 in above equation
⇒−1=

2

3

+c
⇒c=

−5

3

Put the value of c in equation (1).
⇒y=

2

3

x−

5

3

⇒ 3y = 2x - 5
⇒ 2x - 3y = 5 is the equation of other diagonal.
The point (1, -1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then the equation of the other diagonal is 2x - 3y = 5