About This Chapter
Understanding Analytical Geometry - Chapter Summary
Top instructors in this chapter simplify the process of understanding analytical geometry. Review fun and engaging lessons to boost your knowledge of the Cartesian coordinate system, learn how to write equations in standard form, and study measurements of angles and lengths and much more. Upon completion of this chapter, you will have the knowledge to:
- Plot points and graph lines using the Cartesian coordinate system
- Find the distance between two points as well as a point and a line
- List and describe properties of concurrent lines in a triangle
- Convert between two forms of equations for a circle
- Determine the measurements of angles and lengths involving tangents, chords and secants
- Solve real-world problems using parametric equations
- Write the equation of a parabola, ellipse and hyperbola in standard form
- Graph in three dimensions
Study analytical geometry your way by choosing lessons to review, navigating them in any order, and visiting them as often as you'd like until you gain full comprehension. All lessons are available around-the-clock and can be viewed using any computer or mobile device. Lesson quizzes and a chapter exam are available to assess your knowledge of analytical geometry. If you develop questions about specific lesson topics while studying this chapter, feel free to send them to our experts.
1. The Cartesian Coordinate System: Plotting Points & Graphing Lines
Watch this video lesson to see how useful the Cartesian coordinate system is. Learn how points are labeled and how you can plot points and graph lines using the system.
2. How to Find the Distance Between Two Points
After watching this video lesson, you will be able to find the distance between any two points on the coordinate plane. Learn what information you and how to plug them in to your formula.
3. How to Find the Distance Between a Point & a Line
Finding the distance from a point to a line is useful in many science and engineering applications. In this lesson, we calculate this distance using a formula, as well as with some fundamental concepts from geometry and algebra.
4. Properties of Concurrent Lines in a Triangle
Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.
5. How to Find the Equation of a Circle
There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.
6. Measurements of Angles Involving Tangents, Chords & Secants
When lines and circles meet, angles are formed. Fortunately, we can determine the measure of these angles, whether they're formed by tangents, secants or chords, just by knowing the measure of the created arcs.
7. Measurements of Lengths Involving Tangents, Chords and Secants
The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.
8. Parametric Equations in Applied Contexts
Watch this video lesson to learn how you can use parametric equations to help you solve real world problems such as the path of a moving object. Learn how to form parametric equations to model the real world.
9. How to Write the Equation of a Parabola in Standard Form
After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola. Learn what these two points are and how they relate to the parabola.
10. How to Write the Equation of an Ellipse in Standard Form
In algebra, we have equations that make our life so much easier. Some equations are able to tell us information without hard math. Watch this video lesson to see how the equation of an ellipse does this.
11. How to Write the Equation of a Hyperbola in Standard Form
When it comes to equations in algebra, there is most always a standard form that provides us with useful information. Watch this video lesson to learn how to write the standard form equation of a hyperbola by using information about the hyperbola.
12. Graphing in Three Dimensions: Method & Formula
Graphing in three dimensions can be a tough thing to visualize, but once you get that part down it makes geometry much more useful. In this lesson, we learn how to graph using the z-axis as well.
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