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Expressing Geometric Properties with Equations

Area of a Triangle in the Coordinate Plane

Directions: Use the digits 0 to 9, at most one time each, to fill in ordered pairs for all three points, such that the area of Triangle ABC is closest to 6 square units. A ( ___, ___ ) B ( ___, ___ ) C ( ___, ___ ) Source: Henry Wadsworth

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Midpoint Formula

Directions: Create two pairs of coordinates on the same line segment that have M (3,4) as their midpoint. Source: Dane Ehlert

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Coordinate Parallelograms

Directions: Fill in the x and y coordinates using whole numbers 1-9, without repetition, so that the points make a parallelogram. Source: Daniel Torres-Rangel

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Creating Right Triangles 2

Directions: Using only the whole numbers 1 through 8 (without repeating any number), fill in the coordinates to create the vertices of a right triangle: A(__, __), B(__, __), C(__, __) Extension: Try to do this using only the whole numbers 1 through 6. Source: Erick Lee

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Creating Rectangles 2

Directions: Using only the whole numbers 1 through 8 (without repeating any number), fill in the coordinates to create the vertices of a rectangle: A(__, __), B(__, __), C(__, __), D(__, __). Extension: What is the rectangle with the largest/smallest area/perimeter that you can find? Source: Erick Lee

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Create Squares

Directions: Create a square with one of the vertices at (2,3). Fill in the blanks with whole numbers 0 through 9, using each number at most once, to show the rest of the vertices of the square. Bonus: Find more than one set of vertices. Source: John Mahlstedt

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Finding the Length of a Right Triangle’s Altitude

Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment. Source: Kate Nerdypoo

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Parallel Lines and Perpendicular Transversals

Directions: Using the whole numbers 1 through 9 no more than one time each, fill in the boxes so that 2 of the lines are parallel and the third line is a transversal that is as close to perpendicular to the parallel lines as possible. Source: Shelli Foust and Robert Kaplinsky

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Parallel Lines and Transversals

Directions: Using the whole numbers 1 through 9 no more than one time each, fill in the boxes so that 2 of the lines are parallel and the third line is a transversal. Source: Shelli Foust

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