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

The question is incomplete, the points A and B are:

A = (-2, -4)

B = (6, 1)

We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1

We will find that:

The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is

So we only need to use that general formula:

If you want to learn more, you can read:

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Step-by-step explanation:

The question is incomplete; However

Required

Determine coordinates of P

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

In this case;

So, the coordinates of P is calculated as thus

Hence, the coordinates of P is

it would be 6xy and -16xy.