Notes/Examples for Intro to Coordinate Geometry

History The use of geometry dates back to before the beginning of history. However, it was often used in a very practical manner. It wasn't till about 600 BC that mathematicians began using formal logic and reasoning.

Rene Descartes was the man who is responsible for the Cartesian plane (or the x-y graph). He created it in the early 1600s. Surprisingly, he was a philosopher (considered one of the fathers of philosophy) and used his reasoning and logic skills in mathematics and science. One of his famous quotes is "I think, therefore I am."

Later on in history, Albert Einstein built foundational work in geometry to help create and prove his theory of relativity.

Some definitions to keep in mind throughout this unit: Coordinate plane--a two-dimensional surface on which a coordinate system has been set up; invented by Rene Descartes; also called Cartesian plane, graph, coordinate grid Coordinates--the numbers in an ordered pair that locate a point in the coordinate plane Ordered pair--a pair of numbers, written as (x,y), that represents a point on a coordinate grid Line segment--the part of a line between two points on the line, including the two points X-axis--the horizontal number line on a coordinate grid Y-axis--the vertical number line on a coordinate grid Quadrants, Origin To plot points, always write the x value first and then the y value. Ex. (2, 3) (3, -1) (-2, 3) (-3, -2)

Each of these points represents a point in each of the four quadrants (go through I to IV). -give students coordinates and they have to give the correct quadrant

A few examples: Here are some given points: A(1,1) B(1,4) C(5,4) D(5,1) Join these points and find the area of the figure.

Here are some given points: A(-2,-3) B(-6,-3) C(-2,-7) Find the missing point to make a square. Calculate the area.

Draw this one on the overhead and let students work through it. Given points A(3,1) B(-1,3) C(-3,0) D(1,-1) find the area of the polygon ABCD Hint: area of polygon = area of rectangle - total area of shaded triangles