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