Page 1 of 4

Define and Discuss on

Midpoint Formula

www.AssignmentPoint.com

Page 2 of 4

Numerically, the midpoint of a segment can be considered to be the average of its

endpoints. This concept helps in remembering a formula for finding the midpoint of a

segment given the coordinates of its endpoints. Recall that the average of two numbers is

found by dividing their sum by two.

Theorem 102: If the coordinates of A and B are ( x  1 , y  1 ) and ( x  2 , y  2 ) respectively, then

the midpoint, M, of AB is given by the following formula (Midpoint Formula).

Example 1: In Figure 1, R is the midpoint between Q(−9, −1) and T(−3, 7). Find its

coordinates and use the Distance Formula to verify that it is in fact the midpoint of QT .

Page 3 of 4

Figure 1 Finding the coordinates of the midpoint of a line segment.

By the Midpoint Formula,

By the Distance Formula,

Because QR = TR and Q, T, and R are collinear, R is the midpoint of QT

Example 2: If the midpoint of AB is (−3, 8) and A is (12, −1), find the coordinates of B.

Let the coordinates of B be ( x, y). Then by the Midpoint Formula,