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