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**4.7 Triangles and Coordinate Proof**

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**Ex. 1: Placing a Rectangle in a Coordinate Plane**

Place a 2-unit by 6-unit rectangle in a coordinate plane – many possible answers here! One possible answer: One vertex is at the origin, and three of the vertices have at least one coordinate that is 0.

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**Ex. 1: Placing a Rectangle in a Coordinate Plane**

Another possible answer: One side is centered at the origin, and the x-coordinates are opposites.

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**Note: What is the distance formula? What is the midpoint formula?**

Once a figure has been placed in a coordinate plane, you can use the Distance Formula or the Midpoint Formula to measure distances or locate points What is the distance formula? What is the midpoint formula?

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**Ex. 2: Using the Distance Formula**

A right triangle has legs of 5 units and 12 units. Place the triangle in a coordinate plane. Label the coordinates of the vertices and find the length of the hypotenuse.

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**Ex. 3 Using the Midpoint Formula**

In the diagram L is the midpoint of the line segment; find the coordinates of point L. L

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Ex. 4 A right triangle has legs of 7 and 9 units; find the length of the hypotenuse.

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