Show that the straight line joining the points A(0, -1) and B(15, 2) divides the line joining the points C(-1, 2)and D(4, -5) internally in the ratio 2:3.

Given, A(0, -1) B (15, 2) divides the line on points C(-1, 2) and D(4, -5)

To Prove. Straight line divides in the ratio 2:3 internally

The equation of line

Now, Equation of line BC

⇒ 5y + 5 = x

Therefore, x – 5y = 5 ---(1)

Now, Equation of line BC

⇒ 5(y - 2) = -7(x + 1)

⇒ 5y - 10 = -7x - 7

Therefore, 7x +5y = 3 ---(2)

On solving equation (1) and (2)

X = 1 y =

Now, Point of the intersection of AB and CD is O (1,

Let us Assume that AB divides CD at O in the ratio m:n, then

x coordinate of O =

1 =

= 4m – n = m+n

= 4m – m = n+n

= 3m = 2n

= Hence Proved