GOZUNTA
Try it now
All courses Geometry · G-GPE.6 29 of 57
Find the point that partitions a directed segment between two points in a given ratio.

Find the midpoint of a segment

Problem
Find the midpoint of the segment with endpoints \((0,0)\) and \((6,8)\).
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Find a specific skill faster.

Search the curriculum instead of wandering through random problems until the right kind appears.

Create a free account
With paid access

Try the same skill with new numbers.

More variants let you check whether you understand the method instead of remembering one answer.

Compare plans

Hint

Average 0 and 6 for the x-coordinate, and average 0 and 8 for the y-coordinate.

The midpoint formula averages matching coordinates: ((x1+x2)/2, (y1+y2)/2).

Solution walkthrough

01

Use the coordinate midpoint theorem

\[M=((x_1+x_2)/2,(y_1+y_2)/2)\]

The midpoint is halfway in both coordinate directions, so each coordinate is the arithmetic mean of the matching endpoint coordinates.

02

Average the x-coordinates

\[x_M=(0+6)/2=6/2=3\]

The endpoint x-values are 0 and 6; their halfway value is 3.

03

Average the y-coordinates

\[y_M=(0+8)/2=8/2=4\]

The endpoint y-values are 0 and 8; their halfway value is 4.

04

Combine and check

\[M=(3,4);~M-(0,0)=<3,4\ge~(6,8)-M\]

The displacement from the first endpoint to M equals the displacement from M to the second endpoint, confirming that M bisects the segment.

+

Another way

  1. Take half of the displacement <6,8>, obtaining <3,4>, and add it to the starting endpoint.

!

Common mistake

Add and then divide each coordinate sum by 2. The coordinate total (6,8) is the full displacement, not the midpoint.

Solution walkthrough video