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) Eliminate D) (8, 12)

ANSWERA. (8,9)EXPLANATIONThe 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.