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 (horizontal) has a length of \(8\) units (from \((0,0)\) to \((8,0)\)), and the other leg (vertical) has a length of \(2\) units (from \((8,0)\) to \((8,2)\)).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 8\), \(b=2\), and \(c\) is the hypotenuse.
Substitute the values: \(8^{2}+2^{2}=c^{2}\)

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Take the square root of both sides: \(c=\sqrt{68}\)
Simplify \(\sqrt{68}=\sqrt{4\times17} = 2\sqrt{17}\approx 8.25\)

Answer:

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