Question

the diagram shows quadrilateral mnpq. what is the length of line segment mq? 8 units 10 units 11 units 15 units

Explanation:

Step1: Identify right - triangle components

We can consider the right - triangle formed by the vertical and horizontal displacements from N to Q. The vertical displacement from N to Q is 6 units and the horizontal displacement from N to a point directly below N on MQ is 3 units. Also, we know the length of MN is 10 units.

Step2: Use the Pythagorean theorem

Let the length of the part of MQ from M to the point directly below N be $x$. In the right - triangle with hypotenuse MN = 10 and one side 6, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 10$ and $a = 6$. Then $x=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$.

Step3: Calculate the length of MQ

The length of MQ is the sum of the horizontal part from M to the point directly below N and the part from that point to Q. The part from that point to Q is 3 units. So $MQ=8 + 3=11$ units.

Answer:

11 units