Distance between two points and the midpoint

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1,y1) and (x2,y2).

D=(x2x1)2+(y2y1)2


Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

D=(3(1))2+(41)2=

=16+9=25=5

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates:

(x1+x22,y1+y22)


Video lesson

Find the midpoints between the coordinates (-4, -1) and (6,7)