About This Chapter
Three-Dimensional Coordinate Geometry - Chapter Summary
Enjoy access to expert instructors with a wealth of three-dimensional coordinate geometry knowledge. They can help you quickly and easily understand how to plot points on a coordinate plane, graph reflections across axes, find the distance between two points and much more. Review the lessons at your own pace. When finished, you should be able to:
- List and describe three-dimension shapes in geometry
- Describe planes and the polyhedron
- Define and discuss the formula for a tetrahedron
- Find the centroid of a semicircle
- Differentiate between skew lines and parallel lines
- Calculate direction cosines and ratios
- Provide the definition of the Cartesian plane
- Share the meaning of coplanar lines in geometry
Select the lessons you want to view in your sequence of choice, and visit them as many times as you'd like. If you hit a snag during your review and need additional information, send your lesson topic questions to our experts. With each lesson is a short quiz designed to assess your knowledge of its contents. A chapter exam is also available to gauge your overall understanding of three-dimensional coordinate geometry.
1. Overview of Three-dimensional Shapes in Geometry
We are surrounded by three-dimensional shapes. Watch this video lesson to see what some three-dimensional shapes look like, such as a cube, a sphere, a brick, and a cylinder.
2. Plotting Points on the Coordinate Plane
If you'll be working with a graph, otherwise known as the coordinate plane, it's essential to understand how it works. This includes learning the parts of a graph, identifying points and plotting points.
3. 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.
4. How to Graph Reflections Across Axes, the Origin, and Line y=x
A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.
5. Planes and the Polyhedron: Definition and Example
Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.
6. Centroid: Definition, Theorem & Formula
Have you ever wondered how to find the balancing point of a triangle? The answer can be found in this lesson on the centroid of a triangle! We'll learn how medians are used to locate the centroid and then discuss its various properties.
7. Tetrahedron: Definition & Formula
In this lesson, discover the solid called the tetrahedron and use the provided formulas to find its volume and surface area. Special formulas and examples for regular tetrahedra are included.
8. Centroid & Center of Mass of a Semicircle
The centroid is the point at the exact center of an object. If the object has a uniform density, then the center of mass will be located at the centroid. In this lesson, learn how to find the centroid of a semicircle.
9. Skew Lines in Geometry: Definition & Examples
In this lesson, learn the definition of skew lines. You will also learn tips for differentiating skew lines from parallel lines, as well as look at some examples.
10. Direction Cosines & Ratios: Definition & Calculations
Direction cosines and ratios are a way to represent the direction of a 3D vector. In this lesson, learn how to calculate and understand direction cosines and ratios.
11. The Cartesian Plane: Definition & Explanation
The Cartesian plane is like a map grid. Just like the map helps you find the shoe store or post office, the Cartesian plane helps you locate a pair of values.
12. Coplanar Lines in Geometry: Definition & Overview
This lesson will show you how to identify lines that are coplanar in any shape you are given. You will also learn which lines are non-coplanar, and how you can tell the two apart.
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