Question

Find the midpoint of the line segment with the given endpoints. $\left(-\frac{2}{5}, \frac{7}{15}\right)$ and $\left(-\frac{2}{5},-\frac{4}{15}\right)$

Name: Problem 26, Chapter 10: Introductory and Intermediate Algebra for College Students
Uploaded: 2020-07-29T03:29:59-08:00
Duration: 44 s
Channel: Heather Zimmers
Description: Find the midpoint of the line segment with the given endpoints. (-(2)/(5), (7)/(15)) and (-(2)/(5),-(4)/(15))

   Find the midpoint of the line segment with the given endpoints.
$\left(-\frac{2}{5}, \frac{7}{15}\right)$ and $\left(-\frac{2}{5},-\frac{4}{15}\right)$

Introductory and Intermediate Algebra for College Students

Robert Blitzer 6th Edition

Chapter 10, Problem 26

Instant Answer

Solved by Expert Heather Zimmers

07/29/2020

Step 1

Step 1: The midpoint formula is given by: \[X_{m}=\frac{x_{1}+x_{2}}{2}\] \[Y_{m}=\frac{y_{1}+y_{2}}{2}\] where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the coordinates of the endpoints of the line segment. Show more…

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Find the midpoint of the line segment with the given endpoints. $\left(-\frac{2}{5}, \frac{7}{15}\right)$ and $\left(-\frac{2}{5},-\frac{4}{15}\right)$

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Key Concepts

Midpoint Formula

This is a method used in coordinate geometry to determine the exact center point of a line segment defined by two endpoints. It involves calculating the average of the x-coordinates and the average of the y-coordinates of the endpoints, resulting in a new coordinate that is equidistant from both endpoints.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that uses a coordinate system to describe and analyze geometric figures. It allows concepts from algebra and geometry to be combined, making it easier to calculate distances, slopes, and midpoints in a plane.

Averaging

Averaging is a fundamental arithmetic process that involves summing numbers and then dividing by the count of those numbers. In the context of finding the midpoint of a line segment, averaging is used to determine the center point by taking the mean of the corresponding coordinates of the endpoints.

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