Polygons in the Coordinate Plane

welcome to anywhere math I'm Jeff Jacobson and today we're going to talk about polygons in the coordinate plane specifically how to plot them how to draw them in the coordinate plane and then also how to find things like perimeter and area once they're in coordinate plane let's get started okay before we get started with example one you're probably going to want some graph paper or grid paper if all you have is line paper it can work you just have to make sure you're really really organized and have nice straight lines but if you have graph paper like this it's going to make it lot easier so the first thing you're going to want to do obviously is to make your coordinate plane all we're using right now is the first quadrant you can see I've got all the way up from zero up to 15 on my axis and from zero up to 15 on my but if you look nine is the greatest value in my and eight is the greatest in my so you could even just stop at 10 if you want so go ahead first thing draw your axes and remember we only need the first quadrant everything is positive so once you've got that let's read the example so the vertices of quadrilateral are is at 24 is at 39 is at 78 and is at 81 draw the quadrilateral in this coordinate plane so the first thing hopefully you remember that the most important is the value the coordinate comes first then the so when we're looking at these this two is my coordinate and that four is my coordinate so when I'm doing this I'm going to be going over two and then up four okay so I'm going to plot that again said over two right that's the up four that point is going to go right there and then whenever you plot points in coordinate plane always label them so we're just going to call that and that's at 24 next is at 39 again three is the coordinate so on my x- Axis I'm going over three then all the way up to nine and that is where that point is going again label it is at 39 is at seven go over seven up eight right there label that and then finally over eight and up one over eight and up one okay and then label that really it it's pretty simple you just got to make sure that you always remember the coordinate comes first then the and if you want to think about it comes first in the alphabet then maybe that could help you out to remember it so we're almost done We've plotted our vertices now need to draw the quadrilateral and this is pretty simple all you're doing is connecting the dots but you have to do it in order I'm not going to and then to I'm going to right so draw that then to then to and then finally back to and there is my quadrilateral four sides it's closed figure and we're done here's some to try on your own okay here we go with example two so same thing first thing you're going to want to do is create your coordinate plane again we're only using the first quadrant and you don't have to go all the way up to 15 if you look at the number think you go to 10 for each the and axis that would be plenty so let's see the veres of rectangle are is at six is at 76 is at 72 and is at2 draw the rectangle in the coordinate plane and then find its perimeter so first thing let's draw it so we're going to plot our points again first one is at six over one up six it's going to be right there label it just like always next is at 76 go seven over on my x-axis up six it's going to be right there label that is at 76 then 72 over 7 up two right there label and finally is at one two over one up two right there label it now we've got our points they're all plotted remember after that that we have to draw it so you're just connecting the dots to to to and to and it's going to make rectangle okay so we're halfway done we have our our rectangle drawn everything plotted but now we've got to find our perimeter and if you remember perimeter is just the distance around the figure okay imagine if you were walking all the way around it how far would you walk that's the perimeter there's couple ways to do it one formula that we're going to use is you have two lengths right for rectangle you've got two lengths this and this are are congruent they're identical and you have two widths this width and this width are also congruent so let's find out what those lengths and widths are well we'll start with the length here if you see both for and they both have an coordinate of one okay they're both over one but the y-coordinate is different this one is only up two this one's up six so if you want to know the length we just find the difference of those y-coordinates so 6 - 2 is four that's going to be my length Okay I'm going to substitute that in for now how about the width well we can look here from to notice here here that the coordinates are not the same but the coordinates are they are both up two so I'm not going to be subtracting the y-coordinates like did for my length instead I'm subtracting my coordinates I'm finding the difference of seven and one which means this width is six and also if it's something this simple you could also just count the squares right each one of these is just one so you could even count right 1 2 3 4 five six which is what we just said so I'm going to substitute those in is going to be four and my width is six make sure you use parentheses or else it's going to look like 24 but we want 2 * 4 plus 2 * 6 there's two each of those simplify you get 8 + 12 which finally gives you 20 and there's no centimeters and meters these are just units and it's not unit squared because it's perimeter it's just distance so 20 units is your answer and here's one more to try on your own as always thank you so much for watching and if you like this video please subscribe