Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1,?3) lies on the circle centered at the origin and containing the point (0,2).

Exercises from Illustrative Mathematics A set of 2 exercises, commentary, and solutions

Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is two-thirds of the way along each median from the intersected vertex. Using coordinates, students prove the diagonals of a parallelogram bisect one another and meet at the intersection of the segments joining the midpoints of opposite sides.

Teacher and Student versions of full lesson from engageNY

Quadrilateral Classification What if you were given the coordinates of four points that form a quadrilateral? How could you determine if that quadrilateral qualifies as one of the special four-sided figures you learned about in the previous Concepts? After completing this Concept, you'll be able to make such a determination.

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