Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

True or False The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. Given information.

The given statement is:

The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints. 

We need to check whether the given statement is true or false.

Step 2. Determine whether the statement is true or false.

The midpoint of a line segment with endpoints $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

$\text{Midpoint}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

It is clear that, the midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.  

Step 3. Conclusion.

The given statement is true.