Endpoint Formula
The endpoint formula is related to the midpoint formula. The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula. Let us explore the endpoint formula below.
What Is the Endpoint Formula?
Let M (x_{m},y_{m}) be a midpoint for the line joining two endpoints A (x_{1},y_{1}) and B (x_{2},y_{2}). We can use the midpoint formula to solve for either of the endpoints. Given the coordinates of M and A, the coordinates of B can be calculated using the following formula:
x_{m }= \( \dfrac{x_1 + x_2}{2} \), y_{m} = \( \dfrac{y_1 + y_2}{2} \) (From the midpoint formula)
x_{2} = 2x_{m } x_{1}, y_{2} = 2y_{m } y_{1}
Thus, the endpoint formula is,
Endpoint formula of B(x_{2},y_{2}) = (2x_{m } x1, 2y_{m } y_{1})
Note: It is not recommended to learn this formula, rather just find the coordinates of B by just using the midpoint formula.
Let us see the applications of the endpoint formula in the solved examples below.
Solved Examples using the Endpoint Formula

Example 1: M(3, 4) is the midpoint of the line joining points A(5, 2) and B(x, y). Find the coordinates of B using the endpoint formula.
Solution.
M(3, 4) = \( (\dfrac{5+x}{2}, \dfrac{2+y}{2}) \) (Using the midpoint formula)
5 + x = 6, 2 + y = 8
x = 1, y = 6
Answer: Coordinates of B(x, y) = (1, 6), i.e. x = 1 and y = 6

Example 2: C (7, 8) is the center of the circle having a radius = 5 units. A diameter is drawn on this circle, and one of its endpoints is (3, 5). Find the other endpoint of the diameter using the endpoint formula.
Solution.
Let E(x, y) be the other endpoint.
C is the midpoint of a diameter.
C(7, 8) = \( (\dfrac{3+x}{2}, \dfrac{5+y}{2}) \) (Using the midpoint formula)
3 + x = 14, 5 + y = 16
x = 11, y = 11
Answer: The coordinates of the other endpoint E(x, y) is (11, 11)