Midpoint formula

Definition

The midpoint formula calculates the exact center point between two defined points on a coordinate plane. The formula is $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

5 Must Know Facts For Your Next Test

1. The midpoint formula finds the average of the x-coordinates and the y-coordinates of two points.
2. It is used to determine the center point of a line segment in a Cartesian plane.
3. The formula can be extended to three dimensions: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$.
4. The midpoint always lies on the line segment connecting the two original points.
5. Applications include geometry problems, physics problems involving motion, and computer graphics.

Review Questions

• What is the midpoint of points (3, 4) and (7, 8)?
• How do you derive the midpoint formula for three-dimensional space?
• If one endpoint of a segment is (5, -3) and its midpoint is (3, 4), what are the coordinates of the other endpoint?

Related terms

Distance Formula: Calculates the distance between two points in a coordinate plane using $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Slope Formula: Determines the steepness or incline of a line given by $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Coordinate Plane: A two-dimensional surface formed by two perpendicular number lines intersecting at zero.