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Chapter 1: Problem 76

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

Short Answer

Expert verified
To find the midpoint, apply the midpoint formula which involves averaging the x- and y-coordinates of the endpoints. The result is a coordinate pair representing the midpoint.

Step by step solution

01

Understand the Midpoint Formula

For a line with endpoints \(A(x_1, y_1)\) and \(B(x_2, y_2)\), the midpoint formula is \((\frac{x_1 +x_2}{2}, \frac{y_1 + y_2}{2})\). This formula comes from the idea of averages.
02

Apply the Midpoint Formula

Substitute the x and y coordinates of the endpoints into the midpoint formula. This involves adding the two x-coordinates, dividing by 2 to compute the x-coordinate of the midpoint, and then doing the same process for the y-coordinates.
03

Calculation of the Midpoint

Once the calculations from step 2 have been made, the result is the midpoint. The midpoint is a coordinate pair (M, N) that lies straight between the endpoints A and B, splitting the line segment into two equal parts.

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