Midpoint formula

Definition

The midpoint formula calculates the exact center point between two given points on a coordinate plane. It is derived by averaging the x-coordinates and the y-coordinates of the two points.

5 Must Know Facts For Your Next Test

1. The midpoint formula is expressed as $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
2. The midpoint divides a line segment into two equal halves.
3. If both endpoints of a line segment lie on different quadrants, the midpoint will generally fall within one of those quadrants or on an axis.
4. The midpoint formula can also be used in three dimensions: $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right)$. This is beyond basic Algebra but useful to know.
5. Midpoints are often used in geometric proofs and constructions.

Review Questions

• What is the midpoint of the segment connecting (3, -4) and (7, 6)?
• How do you derive the coordinates of a midpoint from two given points?
• In which quadrant does the midpoint lie if one endpoint is at (5, 10) and another at (-3, -6)?

Related terms

Slope: A measure of the steepness of a line, defined as the ratio of vertical change to horizontal change between two points.

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

Coordinate Plane: (Also known as Cartesian Plane) A plane containing an x-axis and y-axis used to graphically represent algebraic equations.