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

We can consider the right - triangle formed by the vertical and horizontal displacements from M to Q. If we assume the horizontal displacement is \(x\) and the vertical displacement is \(y\), and we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse of the right - triangle). Here, we can find the right - triangle with sides related to the given lengths.

Step2: Calculate horizontal and vertical displacements

The vertical displacement from the top - most point to the bottom - most point of the figure (related to the right - triangle for MQ) is \(y = 6\). The horizontal displacement (by observing the parallel sides) is \(x=8\) (since we can use the fact that if we consider the non - vertical and non - horizontal side of length 10 and the vertical side of length 6, the horizontal part of the right - triangle formed is \(\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8\)).

Step3: Apply Pythagorean theorem

Using the Pythagorean theorem \(MQ=\sqrt{x^{2}+y^{2}}\), substituting \(x = 8\) and \(y = 6\), we get \(MQ=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10\).

Answer:

10 units