Question

find the ratio in which line x - 3 Y = 0 divides the line segment joining the points - 2, - 5 and 6, 3 also find the coordinates of the points of intersection

Answer 1

x-3y=0(eq.1)

let the ratio be k:1.

x=6k-2/k+1

y=3k-5/k+1

put value of x and y in eq. 1

6k-2/k+1 - 3(3k-5/k+1)=0

6k-2/k+1 - 9k+15/k+1 = 0

6k-2-9k+15/k+1 =0

13-3k =0

k= 13/3

so,ratio=13:3

x=( 6×13- 2×3)/16

= (78-6)/16

= 9/2

y=(3×13-5×3)/16

= 3/2