Using the Midpoint Formula A line segment. has (x1, y1) as one endpoint and (xm, ym) as its midp

Name: Problem 47, Chapter 1: Precalculus with Limits
Uploaded: 2021-01-22T03:39:52-08:00
Duration: 3 min 36 s
Channel: Chris Trentman
Description: Using the Midpoint Formula A line segment. has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm , and yn m

step 1 We're told that a line segment has a point x1. Y1 at one end point, another point X, M, Y, M at

Question

Using the Midpoint Formula A line segment. has $\left(x_{1}, y_{1}\right)$ as one endpoint and $\left(x_{m}, y_{m}\right)$ as its midpoint. Find the other endpoint $\left(x_{2}, y_{2}\right)$ of the line segment in terms of $x_{1}, y_{1}, x_{m}$ , and $y_{n m}$

   Using the Midpoint Formula A line segment.
has $\left(x_{1}, y_{1}\right)$ as one endpoint and $\left(x_{m}, y_{m}\right)$ as its midpoint.
Find the other endpoint $\left(x_{2}, y_{2}\right)$ of the line segment in
terms of $x_{1}, y_{1}, x_{m}$ , and $y_{n m}$

Precalculus with Limits

Ron Larson 3rd Edition

Chapter 1, Problem 47

Instant Answer

Solved by Expert Chris Trentman

01/22/2021

Step 1

We are asked to find the other endpoint $(x_{2}, y_{2})$ of the line segment. Show more…

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Using the Midpoint Formula A line segment. has $\left(x_{1}, y_{1}\right)$ as one endpoint and $\left(x_{m}, y_{m}\right)$ as its midpoint. Find the other endpoint $\left(x_{2}, y_{2}\right)$ of the line segment in terms of $x_{1}, y_{1}, x_{m}$ , and $y_{n m}$

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Key Concepts

Algebraic Rearrangement in Geometry

Algebraic manipulation is a key component in coordinate geometry where formulas such as the midpoint formula are rearranged to solve for unknown variables. This involves performing operations like multiplication and subtraction to revert the averaging process and obtain the unknown coordinates.

Solving for the Missing Endpoint

When one endpoint and the midpoint of a line segment are known, algebraic manipulation can be used to solve for the unknown endpoint. By setting up equations based on the midpoint formula, one can isolate and compute the coordinates of the missing endpoint.

Midpoint Formula

The midpoint formula in coordinate geometry is used to determine the center point of a line segment. It does so by averaging the x-coordinates and the y-coordinates of the two endpoints independently, which gives the coordinates of the midpoint.

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