Points and Distance

Midpoint Formula

Average the x-coordinates and y-coordinates separately to find the point halfway between two endpoints.

Example

Average coordinates and mark the midpoint on the segment.

highlighted = computed this step

Step 1 — Plot midpoint

Plot A, B, and midpoint M.

Coordinate plot\text{Coordinate plot}
Midpoint formula plotSegment from A(1, 2) to B(4, 7) with midpoint M(5/2, 9/2).ABM

Step 2 — Midpoint x-coordinate

Average the x-coordinates.

xM=(1+4)/2=52x_M=( 1 + 4 )/ 2 = \hlmath{\frac{5}{2}}

Step 3 — Midpoint y-coordinate

Average the y-coordinates.

yM=(2+7)/2=92y_M=( 2 + 7 )/ 2 = \hlmath{\frac{9}{2}}

Step 4 — Midpoint

State the midpoint.

M=(52,92)M=( \hlmath{\frac{5}{2}} , \hlmath{\frac{9}{2}} )
midpoint-formula M = ((x1+x2)/2, (y1+y2)/2)