Question

Find ratio in which a line 2x-3y-9=0 divide line segment (2,3),(3,5)

Answer 1

So, let's use the Two point formula to find the equation of second line. According to the formula,

x- x1/x2-x1= y-y1/y2-y1

LetA(x1,y1) and B(x2,y2)

x-1/2–1= y- 3/7–3

x-1/1= y-3/4

4x-4= y-3

So, 4x-y= 1

This is the equation of second line. Now, we have to solve them simultaneously to find the coordinates of point of intersection. By solving it , as we solve the linear equation in two variable, we get the coordinates as C(10/7, 33/7).Let the ratio be m:n

By using the formula for internal division,

X=mx2-nx1 /m+n

10/7= 2m-n/ m+n

10(m+n)= 7(2m-n)

10m+10n= 14m-7n

10n+7n= 14m-10m

17n= 4m

m/n=17/4

So, the ratio is 17:4.