Coordinate Geometry

Question

The point M(2,3) is given. Find the coordinates of the endpoints of four noncollinear segments that have point M as their midpoint. If you know that a segment with midpoint M has length 6, how many possible noncollinear segments can you find? Explain your reasoning.

Answer 1

Using the midpoint formula you need to identify how many non collinear segments there are?

This is the midpoint formula:

(x1+x2 , y1+y2)

______ _____

2 2

So if you Apply this formula you can figure out that every diameter in the circle will have non collinear segments that has the coordinates (2,3) in it.

Answer 2

Use (2,3) as the center of a circle.

Every diameter of that circle will have (2,3) as its midpoint.