UPSC NDA Math Model Paper 9

The line has the slope -1 and passes through (2, 4)
∴ Equation of the perpendicular line is
(y−y1)=m(x−x1)
⇒y−4=−1(x−2)
⇒y=−x+6 .......(i)
Slope (m1)=−1 and c1=6
Now for the slope of perpendicular line (m2)
m1×m2=−1
⇒−1×m2=−1
⇒m2=1
Perpendicular line has the slope 1 and passes through (−1,3)
∴ Equation of the perpendicular line is
(y−y1)=m(x−x1)
⇒y−3=1(x−(−1))
⇒y=x+4 .......(ii)
Adding (i) and (ii)
⇒ 2y = 10
⇒ y = 5
Putting y in equation (ii)
5 = x + 4
⇒ x = 1
∴ The point of intersection is (1, 5)