Question

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

Explanation:

Step1: Determine the lengths of the two legs

From the coordinate plane, one leg is along the x - axis from \((0,0)\) to \((8,0)\), so its length \(a = 8\). The other leg is from \((8,0)\) to \((8,2)\), so its length \(b=2\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse. Substitute \(a = 8\) and \(b = 2\) into the formula: \(c=\sqrt{8^{2}+2^{2}}=\sqrt{64 + 4}=\sqrt{68}\). Simplify \(\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}\approx 8.25\)

Answer:

The length of the hypotenuse is \(2\sqrt{17}\approx8.25\)