Question

The line 2x - 5y + 31 = 0 bisects the join of (-4,5) and (P, 9). Find the value of p.

Answer 1

Let the point of intersection of AB and the line 2x-5y+31 =O be the point R ( a,b)

Also, given the line 2x - 5y+31 =0 bisects the line segment AB

AR : RB = 1 : 1

Coordinates of R are, 

R (a,b) = R `((-4 + "p")/2 , (5 + 9)/2) = R ((-4 + "p")/2 , 7)`

R (a,b) lies on the line 2x - 5y + 31 = 0

R will satisfy the equation of the line

2`((-4 + "p")/2)` - 5(7) + 31 = 0

⇒ (-4 + p) - 4 = 0

⇒ p = 8