Hovedinnhold
Math
Common Core Math
High School: Geometry: Expressing Geometric Properties with Equations
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.
- Circle equation review
- Features of a circle from its expanded equation
- Features of a circle from its expanded equation
- Features of a circle from its graph
- Features of a circle from its graph
- Features of a circle from its standard equation
- Features of a circle from its standard equation
- Graph a circle from its expanded equation
- Graph a circle from its features
- Graph a circle from its standard equation
- Graphing a circle from its standard equation
- Graphing circles from features
- Write standard equation of a circle
- Writing standard equation of a circle
Derive the equation of a parabola given a focus and directrix.
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
- Center & radii of ellipses from equation
- Ellipse standard equation & graph
- Equation of a hyperbola from features
- Equation of an ellipse from features
- Foci of a hyperbola from equation
- Foci of an ellipse from equation
- Foci of an ellipse from radii
- Graph & features of ellipses
- Vertices & direction of a hyperbola
Use coordinates to prove simple geometric theorems algebraically.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
- Parallel & perpendicular lines from equation
- Parallel & perpendicular lines from graph
- Parallel & perpendicular lines from graph
- Parallel lines from equation
- Parallel lines from equation (example 2)
- Parallel lines from equation (example 3)
- Perpendicular lines from equation
- Proof: parallel lines have the same slope
- Proof: perpendicular lines have negative reciprocal slope
- Write equations of parallel & perpendicular lines
- Writing equations of perpendicular lines
- Writing equations of perpendicular lines (example 2)
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.