Question

The line 4x + 3y = 11 bisects the join of ( 6,m) and (p,9). Find the value of m.

Answer 1

Let the point of intersection of AB and line 4x+4y= 11 be the point P (a,b ),

Also given 4x+3y = 11 bisects line segment AB

.AP : PB = 1 : 1

Coordinates of P are,

P(a,b) = P `((6 + 4)/2 , ("m" - 9)/2)` = P `(5, ("m" - 9)/2)`

Since P(a,b) lies on the line 4x+3y= 11, `therefore` P will satisfy the equation of line

4(5) + 3 `((m - 9)/2)` = 11

`(3"m" - 27)/2` = 11 -20

⇒ 3m - 27 = -18

⇒ 3m = 9

⇒ m = 3