ANSWER
B. (5.75, 0)
EXPLANATION
If 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]
