Finding the Midpoint of a Segment Using the Midpoint Formula – Example and Explanation

midpoint of a segment

The midpoint of a segment is the point that divides the segment into two equal halves

The midpoint of a segment is the point that divides the segment into two equal halves. It is the point that is equidistant from both endpoints of the segment.

To find the midpoint of a segment, you can use the midpoint formula. The formula is:

Midpoint = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Here, (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the segment.

Let’s consider an example to understand how to find the midpoint of a segment.

Example: Find the midpoint of the segment with endpoints A(-3, 2) and B(5, -6).

Solution:
Using the midpoint formula, we have:

x₁ = -3, y₁ = 2 (coordinates of A)
x₂ = 5, y₂ = -6 (coordinates of B)

Applying the midpoint formula:

Midpoint = [((-3 + 5) / 2), ((2 + -6) / 2)]
= [(2 / 2), (-4 / 2)]
= [1, -2]

Therefore, the midpoint of the segment with endpoints A(-3, 2) and B(5, -6) is M(1, -2).

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