Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.A. (3, 1)B. (5,3/4)C. (10, 5)D. (6, 2)

ANSWERThe correct answer is B.EXPLANATIONIf the point B(x,y) partitions [tex]A(x_1,y_1)[/tex]and[tex]C(x_2,y_2)[/tex]in the ratio m:n then, then we have [tex]x = \frac{mx_2+nx_1}{m + n} [/tex]and[tex]y= \frac{my_2+ny_1}{m + n} [/tex]We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.This implies that:[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex][tex] \implies \: x = \frac{55 - 15}{8} [/tex][tex] \implies \: x = \frac{40}{8} = 5[/tex][tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex][tex]y = \frac{0 + 6}{8} [/tex][tex]y = \frac{6}{8} = \frac{3}{4} [/tex]Therefore the coordinates of B are [tex](5, \frac{3}{4} )[/tex]