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4.7 Triangles and Coordinate Proof

Explore how to place a 2-unit by 6-unit rectangle in a coordinate plane and discover multiple possible answers. Learn about the Distance Formula and the Midpoint Formula to measure distances and locate points. Then, use these concepts to place a right triangle in a coordinate plane, label its vertices, and find the length of the hypotenuse.

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4.7 Triangles and Coordinate Proof

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  1. 4.7 Triangles and Coordinate Proof

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

  3. Another possible answer: One side is centered at the origin, and the x-coordinates are opposites. Ex. 1: Placing a Rectangle in a Coordinate Plane

  4. Note: • 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?

  5. 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. Ex. 2: Using the Distance Formula

  6. In the diagram L is the midpoint of the line segment; find the coordinates of point L. Ex. 3 Using the Midpoint Formula L

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

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