Chapter 5: Q. 11 (page 199)

In the following figure, a trapezoid $A B C D$ has a median $\bar{M N}$ . If $A B = 5 i + 7 k, D C = 9 j - 3 k$ then find.

Short Answer

Expert verified

The measure of $M N = 7 j + 2 k$ 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 $M N$ is the median and $A B = 5 i + 7 k, D C = 9 j - 3 k$ $A B = 5 i + 7 k, D C = 9 j - 3 k$ .

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

$\begin{matrix} M N = \frac{A B + D C}{2} \\ = \frac{5 j + 7 k + 9 j - 3 k}{2} \\ = \frac{14 j + 4 k}{2} \\ M N = 7 j + 2 k \end{matrix}$

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

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In the following figure, a trapezoid $A B C D$ has a median $\bar{M N}$ . If $A B = 5 i + 7 k, D C = 9 j - 3 k$ then find.

Short Answer

Step by step solution

Step 1- Apply the concept of midsegment theorem.

Step 2- Check the figure.

Step 3- Step description.

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In the following figure, a trapezoidABCDhas a medianMN¯. IfAB=5i+7k,DC=9j−3k then find.

Short Answer

Step by step solution

Step 1- Apply the concept of midsegment theorem.

Step 2- Check the figure.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

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In the following figure, a trapezoid $A B C D$ has a median $\bar{M N}$ . If $A B = 5 i + 7 k, D C = 9 j - 3 k$ then find.