Understanding the Midpoint Formula | How to Find the Coordinates of a Midpoint in Geometry

midpoint

The midpoint is a point that is exactly in the middle of a line segment

The midpoint is a point that is exactly in the middle of a line segment. It divides the line segment into two equal halves. The midpoint is equidistant from both ends of the line segment.

To find the coordinates of the midpoint, you can use the midpoint formula. Suppose you have two points on a line segment, (x₁, y₁) and (x₂, y₂). The coordinates of the midpoint, which we’ll call (x, y), can be calculated using the following formulas:

x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2

For example, let’s say you have two points A(2, 4) and B(8, 12) on a line segment. To find the midpoint of this line segment, you can use the midpoint formula:

x = (2 + 8) / 2 = 10 / 2 = 5
y = (4 + 12) / 2 = 16 / 2 = 8

Therefore, the midpoint of the line segment AB is (5, 8).

The midpoint is important in geometry and can be used to prove various theorems and properties. It is also useful in many applications, such as finding the center point of a rectangle or dividing a line segment into equal parts.

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