A formula for finding the point exactly halfway between two points in the coordinate plane, by averaging their coordinates.
Finding the midpoint is like finding the average position. If two friends live at different addresses on the same street, the midpoint is the house number exactly halfway between them—the average of their two house numbers. In 2D, you just average both coordinates independently.
Showing a random 20 of 50 problems.
Example 1
hard
Show that the diagonals of the quadrilateral with vertices A(1,1), B(7,2), C(9,6), D(3,5) bisect each other, and therefore the quadrilateral is a parallelogram.Both diagonals share midpoint M. Find it and confirm the quadrilateral is a parallelogram.
Example 2
easy
Find the midpoint of the segment joining (−5,3) and (7,−1).Find the midpoint M of segment AB.
Example 3
medium
A segment from (2,2) to (14,2) is divided into a midpoint, then each half is bisected again. List the three division points.
Example 4
medium
Find the centroid of a triangle with vertices (0,0), (6,0), (3,9).Find the centroid G of triangle ABC.
Example 5
medium
Find the midpoint in 3D of (1,2,3) and (5,8,11).
Example 6
easy
Find the midpoint of (a,b) and (c,d).
Example 7
easy
What is the midpoint formula for points (x1,y1) and (x2,y2)?
Example 8
medium
A segment from (0,0) to (12,0) is divided by its midpoint, then each half is bisected again. List the three division points.
Example 9
easy
Find the midpoint of (0,0) and (8,6).Find the midpoint M of OA.
Example 10
medium
Points (1,2) and (7,k) have midpoint with y-coordinate 5. Find k.
Example 11
hard
Three consecutive vertices of a parallelogram are A(0,0), B(5,1), C(7,4). Find the fourth vertex D.Three vertices of a parallelogram are given. Find vertex D.
Example 12
easy
Find the midpoint of (1.5,2.5) and (4.5,7.5).
Example 13
medium
A median of a triangle goes from vertex A(2,1) to the midpoint of side BC, where B(6,3) and C(4,9). Find the median's endpoint.Find M, the midpoint of BC, where the median from A meets BC.
Example 14
medium
Find the center of a circle whose diameter has endpoints (2,3) and (8,11).Find the center of the circle with diameter AB.
Example 15
easy
Find the midpoint of (−4,2) and (2,−6).Find the midpoint M of AB.
Example 16
medium
The midpoint of segment PQ is M(3,−1). If P=(−2,4), find the coordinates of Q.Midpoint M(3,−1) and endpoint P(−2,4) are given. Find Q.
Example 17
medium
Points (2,k) and (8,7) have midpoint with y-coordinate 5. Find k.
Example 18
challenge
Three consecutive vertices of a parallelogram are (1,1), (4,2), (6,5). Find the fourth vertex.Three vertices A, B, C of a parallelogram are given. Find the fourth vertex D.
Example 19
medium
The midpoint of segment AB is (4,5). If A=(−2,3), find B.A(−2,3) and midpoint M(4,5) are given. Find B.
Example 20
hard
Given A(2,3) and the midpoint of AB is (5,7), find B, then verify AM equals MB using the distance formula.A(2,3) and midpoint M(5,7) are given. Find B.