Chapter E, Problem 5.8EX

To determine

To find: The length of $\overrightarrow{MN}$ .

Answer to Problem 5.8EX

The length of $\overrightarrow{MN}$ is $6$ .

Explanation of Solution

Given information: In $\Delta ABC,AB=8,BC=10,AC=12.$ M is the midpoint of $\overrightarrow{AB}$ and N is the midpoint of $\overrightarrow{BC}$ .

In $\Delta ABC,AB=8,BC=10,AC=12.$ M is the midpoint of $\overrightarrow{AB}$ and N is the midpoint of $\overrightarrow{BC}$ .

The midpoint theorem states that if a line segment joining the midpoints of two sides of triangle, then the length of that line is half of the length of third line.

In the given question, M is the midpoint of $\overrightarrow{AB}$ and N is the midpoint of $\overrightarrow{BC}$ .

Then the line MN must be parallel to AC and length of MN is half of the length of AC

  $\begin{array}{l}MN=\frac{12}{2}\\ MN=6\end{array}$