A line segment has an endpoint at (4, 6), the midpoint of the line segment is (1, 5). What are the coordinates of the point at the other end of the line segment?

Solution:

Let (X₁, Y₁) be one end point of the line segment that  represents (4, 6).

Let (X₂, Y₂) be the other end point which has to be found out.

Let (Xm, Ym) be the coordinates of the midpoint of the line segment which are given as (1,5)

It then can be stated:

X_m = (X₁ + X₂) / 2      (1)

Y_m = (Y₁ + Y₂) / 2        (2)

Since Xm = 1 and X1 = 4 we can write equation (1) as

1 = (4 + X₂)/2

2 = 4 + X₂

X₂ = -2

Since Y_m = 5 and Y₁ = 6 we can write equation (2) as

5 = (6 + Y₂)/2

10 = 6 + Y₂

Y₂ = 10 - 6 = 4

Therefore the other endpoint of the line (X₂, Y₂) is (-2, 4).Answer

---

A line segment has an endpoint at (4, 6), the midpoint of the line segment is (1, 5). What are the coordinates of the point at the other end of the line segment?

Summary

The coordinates of the point at the other end of the line segment are (-2, 4).