# Ch 12: High School Geometry: Analytical Geometry

### About This Chapter

## Analytical Geometry - Chapter Summary and Learning Objectives

In these lessons, you'll start with a foundation of graphing basics and then build a wider understanding of analytical geometry concepts. Learn how to calculate the slopes of various types of lines and to complete analytic geometry proofs. Practice using several different kinds of formulas to determine a midpoint and distance. While investigating the Cartesian coordinate system, you can learn to master plotting points and graphing lines using a table. In these lessons, you can learn how to perform all of these calculations and build a solid knowledge of geometry graphing basics. This chapter is designed to teach you:

- Graphing quadrants, axes, ordered pairs, origins, and intercepts
- Plotting points and graphing lines using a table
- Application of the midpoint formula
- Application of the distance formula
- The definitions and processes for calculating the slopes of lines and using point-slope and slope-intercept forms of lines
- The steps for preparing and completing analytic geometry proofs

Video | Objective |
---|---|

What Are the Different Parts of a Graph? | Learn graphing basics: quadrants, axes, ordered pairs, origins, intercepts. |

The Cartesian Coordinate System | Explain how to plot points. Learn to graph lines using a table. Learn to graph lines using x- and y-intercepts. |

How to Use the Midpoint Formula | Learn how to use the midpoint formula. |

How to Use the Distance Formula | Learn how to use the distance formula. |

Slope, Equation of a Line | Define and explain how to calculate the slope of a line. Discuss how to use point-slope form of a line and slope-intercept form of a line. Demonstrate how to determine slopes of parallel and perpendicular lines. |

Geometric Proofs for Polygons | Discuss how to prepare and complete analytic geometry proofs. |

### 1. What Are the Different Parts of a Graph?

Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need.

### 2. 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.

### 3. 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.

### 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. Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

Being able to calculate the slope of a line is a very useful skill to have. Why? Watch this video lesson to find out and learn how to find the slope when working with various equations and various lines.

### 6. Geometric Proofs for Polygons

Watch this video lesson to learn why it is important for you to learn how to do formal proofs in geometry. Also learn how to set up a proof and how to successfully execute one.

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### Other Chapters

Other chapters within the Geometry: High School course

- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry