ANSWER
A. (8,9)
EXPLANATION
The point that divides,
[tex]A(x_1,y_1), B(x_2,y_2)[/tex]
in the ratio m:n is given by
[tex]x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex]y= \frac{my_2 + ny_1}{m + n} [/tex]
The given points are A(0,15) B(20,0)
the ratio is 2:3.
This implies that, m=2,n=3.
[tex]x_1=0,x_2=20,y_1=15,y_2=0[/tex]
We plug in the values to get:
[tex]x = \frac{2 \times 20 + 3 \times 0}{2+ 3} [/tex]
[tex]x = \frac{40}{5} = 8[/tex]
[tex]y= \frac{2 \times 0 + 3 \times 15}{2+ 3} [/tex]
[tex]y= \frac{45}{5} = 9[/tex]
Hence the required point is
(8,9)
The correct answer is A.
