Question

semester a
which expression can be used to determine the length of segment zy?
$sqrt{8^{2}-3^{2}}$
$sqrt{8^{2}+3^{2}}$
$8^{2}+3^{2}$
$8^{2}-3^{2}$

Explanation:

Step1: Determine the lengths of the legs of the right - triangle

From the graph, the horizontal distance (one leg of the right - triangle) between \(Z\) and \(X\) is \(|3-(- 5)|=8\) units, and the vertical distance (the other leg of the right - triangle) between \(X\) and \(Y\) is \(|4 - 1|=3\) units.

Step2: Apply the Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 8\), \(b = 3\), and \(c = ZY\). So, \(ZY=\sqrt{8^{2}+3^{2}}\)

Answer:

\(\sqrt{8^{2}+3^{2}}\) (the second option)