UPSC NDA Math Model Paper 4

The mid-point divides a line in the ratio 1 : 1 internally.

∴ The co-ordinates of the midpoint (M) of points (1, 3) and (1, -7) will be: M(

1×1+1×1

1+1

,

1×3+1×(−7)

1+1

) =M(1,−2)
The equation of the line parallel to the line 2x−3y−7=0 can be assumed to be k(2x−3y)−7=0.
Since this line passes through M(1, -2), we will get:
k[2(1)−3(−2)]−7=0
⇒k(2+6)−7=0
⇒k=

7

8

The equation, therefore, is
:k(2x−3y)−7=0
⇒

7

8

(2x−3y)−7=0
⇒2x−3y−8=0