Find the coordinates of P so that P partitions the segment AB in the ratio 6:2 if A(−4,12) and B(9,−4). A. (13.75, -24) B. (5.75, 0) C. (-16, 13) D. (9.75, -12)

ANSWERB. (5.75, 0) EXPLANATIONIf the point P(x,y) partitioned [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex]in the ratio m:n, then [tex]x = \frac{mx_2+nx_1}{m + n} [/tex][tex]y=\frac{my_2+ny_1}{m + n} [/tex]If the coordinates are A(−4,12) and B(9,−4), then:[tex]x = \frac{6 \times 9+2 \times - 4}{6 + 2} [/tex][tex]x = \frac{54 - 8}{8} [/tex][tex]x = \frac{46}{8} [/tex][tex]x = 5.75[/tex][tex]y= \frac{6 \times - 4+2 \times 12}{6 + 2} [/tex][tex]y = \frac{24 - 24}{8} [/tex][tex]y = \frac{0}{24} = 0[/tex]The correct choice is [tex]B. (5.75, 0) [/tex]