Endpoint Calculator
Input the coordinates of a known endpoint and the midpoint to instantly calculate the other endpoint of the line segment.
Find the Missing Endpoint From Midpoint
Endpoint
What Is an Endpoint?
In geometry, a line segment is defined by two endpoints, which are its starting and ending points. If one endpoint and the midpoint of the line segment are known, the other endpoint can be calculated.
How to Calculate the Other Endpoint
Given the midpoint \( M(x_m, y_m) \) and a known endpoint \( A(x_1, y_1) \), the coordinates of the other endpoint \( B(x_2, y_2) \) are calculated using the following formulas: \( x_2 = 2x_m - x_1 \) \( y_2 = 2y_m - y_1 \)
Examples
Example 1: Given the known endpoint \( A(2, 3) \) and midpoint \( M(5, 5) \), find the other endpoint \( B \)
Solution:
\( x_2 = 2 \times 5 - 2 = 8 \)
\( y_2 = 2 \times 5 - 3 = 7 \)
Result: The other endpoint is \( B(8, 7) \)
Example 2: Given the known endpoint \( C(-4, 6) \) and midpoint \( M(3, 2) \), find the missing endpoint \( D \)
Solution:
\( x_2 = 2 \times 3 - (-4) = 10 \)
\( y_2 = 2 \times 2 - 6 = -2 \)
Result: The missing endpoint \( D(10, -2) \)