Question

given directed line segment AB find the coordinates of p such that the ratio of ap to pb is 2:1 plot point p

Answer 1

Answer:

$P(\frac{10}{3}, \frac{-2}{3})$

Step-by-step explanation:

The question is incomplete; However

$A = (-2, -4)$

$B = (6, 1)$

Required

Determine coordinates of P

When line segment is divided in ratios, the following formula calculates the coordinates;

$P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}$

In this case;

$m:n = 2:1$

$(x_1,y_1) = (-2, -4)$

$(x_2,y_2) = (6, 1)$

So, the coordinates of P is calculated as thus

$P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}$

$P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}$

$P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}$

Hence, the coordinates of P is

$P(\frac{10}{3}, \frac{-2}{3})$