Question

find the length of the hypotenuse of the triangle in the coordinate plane.

Explanation:

Step1: Determine the lengths of the two legs

Count the units on the coordinate - plane. The vertical leg length \(a = 6\) (from \(y = 1\) to \(y=-5\)), and the horizontal leg length \(b = 5\) (from \(x=-2\) to \(x = 3\)).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse. Substitute \(a = 6\) and \(b = 5\) into the formula: \(c=\sqrt{6^{2}+5^{2}}=\sqrt{36 + 25}=\sqrt{61}\approx7.81\)

Answer:

The length of the hypotenuse is \(\sqrt{61}\approx7.81\)