Lines, Segments, and Shapes in the Coordinate Plane Introduction

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

How do we derive the equation of a circle?
How can we use coordinates to prove simple geometric theorems algebraically?
What are the slope criteria for parallel and perpendicular lines and how do we prove and apply them?
How can we find the point on a directed line segment between two given points that partitions the segment in a given ratio?
How do we use coordinates to compute the perimeters of polygons?
How do we use coordinates to compute areas of triangles and rectangles?

Key Terms

Distance Formula = $LaTeX: \sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}^{ }$ equation image indicator

Circle - the set of all points equidistant from a given point

Standard form for the equation of a circle: equation image indicator $LaTeX: \left(x-h\right)^2+\left(y-k\right)^2=r^2$

General form for the equation of a circle: equation image indicator LaTeX: ax^2+by^2+cx+dy+e=0

Parallel Lines - two lines that have the same slope

Perpendicular Lines - two lines whose slopes are opposite reciprocals

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

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