# Ch 8: Geometry Basics

### About This Chapter

## Geometry Basics - Chapter Summary and Learning Objectives

Geometry is built on a foundation of basic formulas that include how to find the area of a circle, the midpoint of a line and the distance between two points in space. In this chapter, you will be introduced to these formulas and learn how to use them. The video lessons also cover the formulas you will need for skills such as graphing circles and rewriting an equation in standard form. After completing the lessons in this chapter, you should be able to:

- Find the area and circumference of a circle
- Graph a circle by identifying the formula, center and radius
- Rewrite a general second-degree equation into standard form
- Use the distance formula to calculate the distance between two points in space
- Use the midpoint formula to determine the midpoint of a line segment

Video | Objectives |
---|---|

Circles: Area and Circumference | Use standard formulas to find the area and circumference of a circle. |

Graphing Circles: Identifying the Formula, Center and Radius | Graph a circle by utilizing the correct formulas to determine the center and radius. |

Write Standard Form of an Equation by Completing the Square | Rewrite an equation from a general second-degree equation to standard form. |

How to Use the Distance Formula | Use the distance formula to determine the distance between two points. |

How to Use the Midpoint Formula | Use the midpoint formula to determine the midpoint of a line segment. |

### 1. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 2. Graphing Circles: Identifying the Formula, Center and Radius

Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.

### 3. Write the Standard Form of an Equation by Completing the Square

In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.

### 4. How to Use The Distance Formula

You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!

### 5. How to Use The Midpoint Formula

The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105