Question

which expression can be used to determine the length of segment zy? \\(\bigcirc\\ 8^2 + 3^2\\) \\(\bigcirc\\ \sqrt{8^2 + 3^2}\\) \\(\bigcirc\\ 8^2 - 3^2\\)

Explanation:

Step1: Find coordinates of Z and Y

From the graph, \( Z(-5, 1) \), \( Y(3, 4) \).

Step2: Calculate horizontal and vertical distances

Horizontal distance: \( |3 - (-5)| = 8 \), vertical distance: \( |4 - 1| = 3 \).

Step3: Apply distance formula

Distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \), so \( ZY = \sqrt{8^2 + 3^2} \).

Answer:

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