Find the point, m, that divides segment ab into a ratio of 2: 3 if a is at (0, 15) and b is at (20, 0).

a. (8, 9)
b. (9, 9)
c. (9, 12)
d. (8, 12)

option A

Explanation:

Let,

(x,y) be the coordinate of point M.

Here M divides the line AB in ratio 2:3.

I'll write given information in a standard format so that you can easily apply it in formula:

A(0,15)=A(x1,y1)

B(20,0)=B(x2,y2)

ratio(m1:m2)=2:3

Now we use section formula of internal division to find coordinates of M,

x=(m1 × x2 + m2 × x1)/(m1+m2)

=(2×20+3×0)/(2+3)

=40/5

=8

&,

y=(m1 × y2 + m2 × y1)/(m1+m2)

=(2×0+3×15)/(2+3)

=45/5

=9

Required M(8,9)