Question

Determine the length of the line segment whose midpoint is $(4,-6)$ with one endpoint at $(7,-2)$.

Name: Problem 109, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2020-03-10T00:37:35-08:00
Duration: 31 s
Channel: Zach Steedman
Description: Determine the length of the line segment whose midpoint is (4,-6) with one endpoint at (7,-2).

   Determine the length of the line segment whose midpoint is $(4,-6)$ with one endpoint at $(7,-2)$.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 10, Problem 109

Instant Answer

Solved by Expert Zach Steedman

03/10/2020

Step 1

Step 1: Recall the midpoint formula: The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Show more…

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Determine the length of the line segment whose midpoint is $(4,-6)$ with one endpoint at $(7,-2)$.

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Key Concepts

Midpoint Formula

The midpoint formula is used in coordinate geometry to determine the center point of a line segment. It calculates the average of the x-coordinates and the y-coordinates of the endpoints, providing insight into how two points in the plane relate symmetrically.

Distance Formula

The distance formula, derived from the Pythagorean theorem, measures the straight-line distance between two points in the coordinate plane. It uses the differences between corresponding coordinates to compute the length of the segment, serving as a fundamental tool in geometry.

Finding a Missing Endpoint

When given one endpoint and the midpoint of a line segment, the missing endpoint can be found by reversing the averaging process used in the midpoint formula. This involves solving for the unknown coordinates by doubling the midpoint values and subtracting the known endpoint coordinates, illustrating the utility of algebra in geometric contexts.

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