Question

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).

Answer 1

ANSWER

B. (5.75, 0)

EXPLANATION

If the point P(x,y) partitioned

$A(x_1,y_1)$

and

$B(x_2,y_2)$

in the ratio m:n, then

$x = \frac{mx_2+nx_1}{m + n}$

$y=\frac{my_2+ny_1}{m + n}$

If the coordinates are A(−4,12) and B(9,−4), then:

$x = \frac{6 \times 9+2 \times - 4}{6 + 2}$

$x = \frac{54 - 8}{8}$

$x = \frac{46}{8}$

$x = 5.75$

$y= \frac{6 \times - 4+2 \times 12}{6 + 2}$

$y = \frac{24 - 24}{8}$

$y = \frac{0}{24} = 0$

The correct choice is

$B. (5.75, 0)$