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.
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).
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).
1. Rise & Run (Revamped)
2. Rise & Run
3. Slope Illustrator
4. Slope: Intuitive Introduction (II)
5. Slope: Intuitive Intro and Exploration
6. Parallel Consequence? (VA)
7. Parallel Consequence? (VB)
8. Parallel Lines in the Coordinate Plane (VA)
9. Parallel Lines in the Coordinate Plane (VB)
10. Coordinate Geometry: Quick Investigation
11. Parallel and Perpendicular Lines in the Coordinate Plane