if point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1 then p must have coordinates of?

That means P is the midpoint:

[tex]P=\left(\frac{x_1+x_2}{2}\;,\; \frac{y_1+y_2}{2} \right) \\ \\ P=\left(\frac{-5+1}{2}\;,\; \frac{11+5}{2} \right)=\left(\frac{-4}{2}\;,\; \frac{16}{2} \right) \\ \\ P=(-2\;,\;8)[/tex]

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jainveenamrata jainveenamrata · Answer 2 · 2022-03-25T09:59:10+01:00

If the ratio is 1:1 then the point must be a mid-point. Then the coordinate of the mid-point P is (–2, 8).

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.

If point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1.

We know that if the ratio is 1:1 then the point must be a mid-point.

Let the coordinate of point P be (x, y)

Then we have

[tex]\rm (x,y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})\\\\(x,y) = (\dfrac{-5+1}{2}, \dfrac{11+5}{2})\\\\(x,y) = (\dfrac{-4}{2} , \dfrac{16}{2})\\\\(x,y) =(-2, 8)[/tex]

The coordinate of the mid-point P is (–2, 8).

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567