6 Course 6 of 10
Coordinate geometry
Coordinate geometry turns shapes into equations: a point becomes a pair of numbers, a line a linear equation, a parabola a quadratic. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.
Before you start: Algebra 2 (systems, radicals, quadratic equations) and the Pythagorean theorem.
Unit 1 Points and lines
- 1 The coordinate plane, distance and midpoint Coordinates and quadrants, the distance formula, the midpoint formula, and using them to classify triangles and find missing endpoints. 11 min
- 2 Slope and equations of lines Slope as rate of change, slope-intercept form, point-slope form, standard form, intercepts, and horizontal and vertical lines. 13 min
- 3 Parallel and perpendicular lines Slopes of parallel and perpendicular lines, writing their equations through a given point, perpendicular bisectors, and proving shapes with slopes. 11 min
- 4 Intersections and the distance from a point to a line Finding where two lines intersect, the formula for the distance from a point to a line, the distance between parallel lines, and the area of a triangle from coordinates. 12 min
Unit 2 Parabolas
- 5 Parabolas Parabolas as graphs of quadratics, vertex form and standard form, the vertex and axis of symmetry, and the focus and directrix. 14 min
- 6 Parabolas and lines Finding where a line meets a parabola, using the discriminant to tell secant, tangent and non-intersecting lines apart, and finding tangent lines. 12 min
Unit 3 Circles
- 7 Equations of circles The standard equation of a circle, the general form, completing the square to find the center and radius, and writing equations from given information. 12 min
- 8 Circles and lines Deciding whether a line crosses, touches or misses a circle, finding intersection points, the tangent line at a point, and the length of a chord. 12 min
Unit 4 Ellipses and hyperbolas
- 9 Ellipses The ellipse as a set of points, its standard equation with a horizontal or vertical major axis, vertices, co-vertices, foci, eccentricity and ellipses centered at any point. 13 min
- 10 Hyperbolas The hyperbola as a set of points, standard equations with horizontal and vertical transverse axes, vertices, foci, asymptotes, eccentricity and rectangular hyperbolas. 13 min