key term - 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

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.