Question

In the following figure, a trapezoid$ABCD$has a median$\overline{MN}$. If$AB=5i+7k,DC=9j-3k$ then find.

Short answer

The measure of$MN=7j+2k$units.

Step-by-step solution

Step 1- Apply the concept of midsegment theorem.

The trapezoid midsegment theorem states that the length of the midsegment is equal to the sum of the base lengths divided by 2.

Step 2- Check the figure.

Consider the figure.

Step 3- Step description.

Here$MN$is the median and $AB=5i+7k,DC=9j-3k$$AB=5i+7k,DC=9j-3k$.

Use the mid-segment theorem and find the value of MN as follows:

$\begin{array}{c}MN=\frac{AB+DC}{2}\\ =\frac{5j+7k+9j-3k}{2}\\ =\frac{14j+4k}{2}\\ MN=7j+2k\end{array}$

Therefore, the measure of $MN=7j+2k$units.