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### Course: Integrated math 1>Unit 1

Lesson 1: Overview and history of algebra

# Intro to the coordinate plane

Descartes created a system of two perpendicular axes (the x and y axes) which could be used to plot points in a plane. This enabled the visualization of algebraic equations in geometric form. For example, a linear equation like y = 2x + 1 could be plotted as a line on the coordinate plane, while a quadratic equation like y = x^2 could be plotted as a parabola. This linked algebra and geometry through the use of graphs. Created by Sal Khan.

## Want to join the conversation?

• How do you convert Cartesian coordinates to Polar coordinates?
• First construct a triangle on any point on the Cartesian plane. Then use the Pythagorean theorem to solve for a the hypothenuse. The hypothenuse is the distance between the origin (0,0) and your point. Call that distance r. Next use trigonometry to solve for the angle in between. Once you have the distance r and an angle theta you're done. Just label them (r,theta) just like you would (x,y) and those are your Polar Coordinates.
• I heard a story that Descartes came up with the idea of the coordinate plane while sick in bed. He was looking up at the ceiling tiles and noticing flies moving around. From this he got the idea of using these axes. Is this true?
• I basically heard that the story was that the Descartes was a person who loved to think in a bed and one day his mind was focusing on the place of an object and thought of the Cartesian plane but i don't know that it was a fly for that thank you
• How do you convert cartesian coordinates to polar coordinates?
• To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):
r = √(x² + y²)
θ = tan⁻¹(y/x)
• Mind blown... this is how maths should be taught in schools. Give kids the background and the reasons why before giving them the how. More engaging and interesting.
• this is so true. I'm so much more intrigued by knowing the how, what, and why; it makes me want to learn.
• I always wondered who came up the the Cartesian coordinates. Now I know! I wonder how he came up with these?
• hey guys. I'm going into 8th grade, but skipping the math, and going right into Algebra. Is there things I should know from 8th Grade math before I go into Algebra? I'm a little scared.
• Not really, it's basically the same as pre- algebra. You will probably want to look at slope, intercepts, and maybe angles if you haven't already. Again, algebra is really just what you already know but with more formulas and steps.
• Now we know who made math harder
• Actually a bit easier, because we can now vizualize it than just having to do math dry.
• Why does this have geometry? I thought this is ALGEBRA
• Well, it is algebra. As they say in the video, it is a bridging of the two subjects. Another way of saying it is that some of the things that are a part of algebra are also connected with geometry. Once you do get to geometry, the things from algebra will not be ignored. You can't have it without algebra.