$\"\"$

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The points are $\"\"$ , $\"\"$ and $\"\"$ .

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Calculate lengths of each side of the triangle by using the distance formula,

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$\"\"$ .

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$\"\"$

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Calculate length of the $\"\"$ .

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$\"\"$ and $\"\"$

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Calculate length of the $\"\"$ .

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$\"\"$ and $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Calculate length of the $\"\"$ .

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$\"\"$ and $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Lengths of two sides of the triangle are equal, so the triangle is isosceles triangle.

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$\"\"$

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Graph:

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Draw the coordinate plane.

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Plot the points and connect the plotted points.

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$\"\"$

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Verify the Pythagorean theorem.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ is a right triangle.

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$\"\"$

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$\"\"$ is a isosceles right triangle.