Question

If the line joining (4,5) and (P,-5) is bisected by the line 2x+3y-6=0 then value of p is​

Answer 1

Given : Line 2x + 3y - 6 = 0 is bisected by points (4, 5) and (P, -5).

To find : Value of P

Solution :

If the line bisects the given points, it will move through their mid point.

Mid point of two points joining (x1, y1) and (x2, y2) is given by,

• Mid-point = ((x1 + x2)/2, (y1 + y2)/2)

Therefore, the mid point of given coordinates is,

⇒ Mid-point = [(4+P)/2, (5-5)/2]

⇒ Mid-point = [(4+P)/2, 0]

Now these coordinate must satisfy the given equation of line.

Therefore,

⇒ 2x + 3y - 6 =0

⇒ 2(4 + P)/2 + 3(0) - 6 = 0

⇒ (4 + P) + 0 - 6 = 0

⇒ P = 6 - 4

⇒ P = 2

So required value of P is 2.[tex][/tex]