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Question
The line segment formed by the points (3, 7) and (-7, z) is bisected by the line 3x + 4y =18. Find the value of z.
Solution
Let the point of intersection of AB and the line 3x + 4y = 18 be the point P (a,b)
Also, given the line 3x + 4y= 18 bisects the line segment AB
AP : PB = 1 : 1
Coornating of P are,
P(a,b) = P `((3 -7)/2 , (7 + "z")/2) = "P"(-2 (7 + "z")/2)`
P (a,b) lies on the line 3x + 4y = 18,
P will satisfythe equation of the line
3(-2) + 4 `((7 +"z")/2)`= 18
⇒ 14 + 2z = 24
⇒ 2z = 10
⇒ z = 5
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