If one endpoint of a line segment is at (4, 6) and the midpoint is at (1, 5), what are the coordinates of the other endpoint of the line segment?

To find the coordinates of the other endpoint of the line segment, we can use the formula for the midpoint. The midpoint
(m) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is calculated as follows:

m = ( (x₁ + x₂) / 2 , (y₁ + y₂) / 2 )

In this case, we have:

• Endpoint 1: (x₁, y₁) = (4, 6)
• Midpoint: (m) = (1, 5)

Let’s denote the coordinates of the other endpoint (x₂, y₂). We know:

• Midpoint x-coordinate: 1 = (4 + x₂) / 2
• Midpoint y-coordinate: 5 = (6 + y₂) / 2

Now, we can solve these equations one by one:

Solving for x₂:

1 = (4 + x₂) / 2

Multiply both sides by 2:

2 = 4 + x₂

Subtract 4 from both sides:

x₂ = 2 – 4

x₂ = -2

Solving for y₂:

5 = (6 + y₂) / 2

Multiply both sides by 2:

10 = 6 + y₂

Subtract 6 from both sides:

y₂ = 10 – 6

y₂ = 4

Final Coordinates:

Thus, the coordinates of the other endpoint of the line segment are (-2, 4).