UPSC NDA 2 2016 Mathematics Solved Paper

Equation of given line is
(y−3)=(‌‌

3−1

2−1

)(x−2)
⇒y=2x−1
Slope m1=2 and slope of perpendicular =−

1

2

The perpendicular is also bisector, therefore it will pass through its mid-point.
⇒ Coordinates of mid-point of given line are :
(‌‌

2+1

2

,‌‌

3+1

2

)‌or‌(‌‌

3

2

,2)
So, equation of perpendicular bisector is :
(y−2)=−‌‌

1

2

(x−‌‌

3

2

)
⇒2x+4y−11=0