Use coordinates to prove simple geometric theorems algebraically
Expressing Geometric Properties with Equations
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Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.