Using the Midpoint Formula to Find the Coordinates of the Midpoint on a Coordinate Plane

midpoint formula

The midpoint formula is used to find the coordinates of the midpoint of a line segment on a coordinate plane

The midpoint formula is used to find the coordinates of the midpoint of a line segment on a coordinate plane. The midpoint is the point that lies exactly halfway between the two endpoints of the line segment.

The formula for finding the midpoint is as follows:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

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

Let’s work through an example to understand how to use the midpoint formula:

Example: Find the midpoint of the line segment with endpoint coordinates (-4, 2) and (6, 8).

Solution:

Step 1: Identify the coordinates of the endpoints:
(x1, y1) = (-4, 2)
(x2, y2) = (6, 8)

Step 2: Apply the formula for the midpoint:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Midpoint = [((-4 + 6)/2), ((2 + 8)/2)]

Step 3: Perform the calculations:
Midpoint = [(2/2), (10/2)]

Midpoint = [1, 5]

Step 4: Interpret the result:
The midpoint of the line segment with endpoint coordinates (-4, 2) and (6, 8) is (1, 5).

So, the coordinates of the midpoint of the line segment are (1, 5).

The midpoint formula can be used in various situations, such as finding the center of a circle or determining the halfway point between two locations on a map. It is a helpful tool in geometry and coordinate geometry problems.

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