Plotting Simple Figures on Coordinate Graphs

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  • 0:01 How to Plot the Dots
  • 1:06 Plotting a Rectangle
  • 2:39 Length & Area
  • 3:18 What About a Triangle?
  • 3:59 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.

One of the most basic parts of geometry is learning how to plot simple figures onto a coordinate graph. In this lesson, we learn how to do that, as well as calculate the area and length of the figures we sketched.

How to Plot the Dots

So, you're all excited for math class. After all, you'll be learning about rectangles and triangles on coordinate planes. You rocked the unit on rectangles and triangles last year and look forward to doing the same this year. Whatever this coordinate plane talk is can't be enough to stop you from getting an easy A in math this year.

That is, until you walk into class. On the board aren't the shapes you're used to. In fact, there aren't even shapes on the board at all! Instead, there's a grid and a bunch of numbers in parentheses. So much for finishing homework early and talking with your friends, you think, as you settle into trying to figure all this out.

Luckily, it's not as bad as it looks. That grid is called a coordinate plane, and it allows us to draw shapes with a great deal of precision. It also makes it much easier for us check for area and length. And those numbers in parentheses? They are called points and serve as the boundaries (corners) of our shapes.

Plotting a Rectangle

Let's say that the first problem on your homework is to chart a rectangle. That's easy enough. You are given a set of four points, namely (2, 5), (2, 10), (4, 5), and (4, 10). Those are your corners. So. how do you chart them? In each chart on your homework you notice that there is a thick vertical line with numbers going up and a thick horizontal line with numbers going sideways. These are your axes. The x-axis is the horizontal line, while the y-axis is the vertical line. Each one of your points also has an x number and a y number. The first number in the parenthesis refers to how far the point is from the origin on the x-axis, and the second number refers to how far the point is from the origin on the y-axis. If you've ever played that board game where you try to sink each other's fleets, you get the idea. Oh, and the origin is the point where the x and y axes meet, and it has the point of (0, 0), since it is no distance from itself.

So, enough of that, back to those numbers. For (2, 5), we go to the right two spots and up 5. Then for (2, 10) we go to the right two, but then up 10. For (4, 5) we go to the right 4 spots now, but up 5. Finally, for (4, 10) we go to the right 4 spots, but up 10. By the way, a negative x means you go to the left, and a negative y means you go down. In any case, we end up with our rectangle. All that's left is for you to connect the dots.

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