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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.
Solution
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.
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