Show that the coordinates (x0, y0) of the midpoint of the segment with endpoints 𝐒(x1, y1) and 𝐓

step 1 Hello, welcome to this lesson. In this lesson we've been asked to prove that the midpoint of two

Show that the coordinates (x0, y0) of the midpoint of the...

Show that the coordinates $\left(x_0, y_0\right)$ of the midpoint of the segment with endpoints $\mathbf{S}\left(x_1, y_1\right)$ and $\mathbf{T}\left(x_2, y_2\right)$ are given by

$$
x_0=\frac{x_1+x_2}{2}, \quad y_0=\frac{y_1+y_2}{2}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Arithmetic Mean

The arithmetic mean is a fundamental concept in mathematics that represents the average value of a set of numbers. In the context of the midpoint formula, the arithmetic mean is applied to each coordinate separately, ensuring that the resulting point is equidistant from the endpoints along each axis.

Midpoint Formula

The midpoint of a line segment is the point that divides the segment into two equal parts. The midpoint formula, derived from coordinate geometry, determines the coordinates of this point by taking the arithmetic mean of the corresponding coordinates of the endpoints. This ensures that the distances from the midpoint to each endpoint are equal.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry, involves representing geometric figures and relationships using a coordinate system. It allows the precise description and analysis of shapes, lines, and points in a plane using ordered pairs, and forms the basis for connecting algebraic equations with geometric figures.

Transcript

Please give Ace some feedback