Question

The line segment formed by two points A (2,3) and B (5, 6) is divided by a point in the ratio 1 : 2. Find, whether the point of intersection lies on the line 3x - 4y + 5 = 0.

Answer 1

Let the point on x-axis be P (x,y) which divides the line segment AB in the ratio 1 : 2, 

i.e. AP : PB = 1 : 2

Coordinates of P are,

P (x,y) = P `(( 5 + 4)/3 , ( 6 + 6)/3)`

x = 3, y=4

If P (x,y) lies on the line 3x - 4y + 5 =O, then it will satisfy the equation of the line.

LHS = 3 (3) - 4 ( 4)+ 5 = 9 - 9 = 0 = RHS

Yes, the point Plies on the line 3x - 4y + 5 = 0.