LAC 28:CXLII.2307. Expressing Geometric Properties with Equations

A. Translate between the geometric description and the equation for a conic section. 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. B. Use coordinates to prove simple geometric theorems algebraically. 1. Use coordinates to prove geometric theorems algebraically. 2. Determine the slope criteria for parallel and perpendicular lines and use them to solve geometric problems 3. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Apply ratio thinking to find the midpoint of the given line segment. 4. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.