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.

Answer 1

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