ACGC - Algebraic Connections to Geometric Concepts Overview

Algebraic Connections to Geometric Concepts Introduction

image of streets and houses with the caption: "what kind of shapes do you see?"You are probably familiar with concepts such as parallel and perpendicular lines, perimeter, and area. However, you may not have combined these with your knowledge of the coordinate plane. That's exactly what we will do in this module! We can use coordinates to prove many theorems that you are already familiar with, as well as to find the area and perimeter of a variety of shapes - it's the perfect blend of Algebra and Geometry!

Essential Questions

  • What are the slope criteria for parallel and perpendicular lines and how do we prove and apply them?
  • How do we find the distance of a line segment plotted on the coordinate plane?
  • How do we use coordinates to compute the perimeters of polygons?
  • How do we use coordinates to compute areas of triangles and rectangles?
  • How do we use the slope, distance, and midpoint formulas to solve real-world problems? 

Key Terms

Distance Formula  = LaTeX: \sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}^{ }√(x2−x1)2+(y2−y1)2

Midpoint Formula = LaTeX: (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})(x2+x12,y2+y12)

Point-Slope Form = LaTeX: y-y_1=m(x-x_1)y−y1=m(x−x1)

Slope Formula = LaTeX: \frac{y_2-y_1}{x_2-x_1}y2−y1x2−x1

Parallel Lines  - two lines that have the same slope

Perpendicular Lines  - two lines whose slopes are opposite reciprocals

Negative Reciprocal -  Swap the numerator and denominator and add a negative sign. Example: LaTeX: \frac{2}{3}=-\frac{3}{2}23=−32

Line Segment  - a part of a line bounded by two distinct endpoints

 IMAGES CREATED BY GAVS