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Chapter 5: Q. 11 (page 199)

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

Short Answer

Expert verified

The measure ofMN=7j+2kunits.

Step by step solution

01

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.

02

Step 2- Check the figure.

Consider the figure.

03

Step 3- Step description.

HereMNis the median and AB=5i+7k,DC=9j鈭�3kAB=5i+7k,DC=9j鈭�3k.

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

MN=AB+DC2=5j+7k+9j鈭�3k2=14j+4k2MN=7j+2k

Therefore, the measure of MN=7j+2kunits.

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