Geometry: Expressing Geometric Properties with Equations Archive

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference…

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four…

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the…

Find the point on a directed line segment between two given points that partitions the segment in a given…

Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles…

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to…

Derive the equation of a parabola given a focus and directrix.