Ch 9 Lesson 5 Polygons on the Coordinate Plane

hi students this is chapter nine lesson five and the title of this lesson is polygons on the coordinate plane just to quickly review polygon remember there's three things that make something polygon closed figure straight sides and lines that don't cross if it meets all three it's polygon and the coordinate plane is something that we've dealt with lot in the past as well so some repeat ideas in this lesson and then putting some things we've done in the past together along with couple of new ideas as well okay first example we're going to look at is building shape on coordinate plane so the example is this rectangle has vert has these vertices okay now vertex of polygon is where two sides come together like that that's that point in the corner right there that is vertex vertices is just the plural of vertex so rectangle has these vertices point is at the ordered pair 1 comma 1 and then we've got at 5 1 5 comma 1 we have Point at 5 comma 4 ordered pair 5 4 and we also have at 1 comma 4 so we are going to build rectangle on coordinate plane using these ordered pairs and these are the corners or vertices of the rectangle so let's build coordinate plane so I'm gonna use ruler here like that okay so there is coordinate plane and this is the y-axis this is the x-axis this 0 0 and 1 2 3 4 5 6 up okay now remember that when we are our little guide over here for coordinates is it is always value first value second and this is super important your guide is right or left first depending on if it's positive or negative you can never go up or down on that first number the second number moves you up or down so most of you are doing really well with this but this is great review for some of you so now let's get these vertices on our coordinate plane point is at 1 1 so I'm going to go over 1 up 1 and I'll label that and is at 5 1 so I'm going to go over 5 1 2 3 4 5 up 1 this is point or vertex Point is 5 4 over 5 up 4 and finally is over 1 up four so here's now it told us that this made rectangle so if we put our vertices onto the coordinate plane and it did not make rectangle right away we would know that something's not right okay so ABCD we plotted those vertices connect the points and we do have rectangle so let's say we were asked to find the perimeter of that rectangle find the perimeter from lesson ago the perimeter is the distance around the outside so we're building fence around this figure so to do that the perimeter would be this is one I've got one two three four units of fence that way and one two three units of fence on that side four more here three more here four plus three plus four plus three would have seven and seven fourteen units of fence or the perimeter would be 14 units so that is some of the problems you're going to practice today is you'll have shape you'll have ordered pairs we'll graph those points on the coordinate plane see what the shape is and do what it says like find the perimeter of the shape that you just that you just graphed okay next what if I'm going to look at the same square or I'm sorry same rectangle four by three rectangle and in this example what if we changed the scale or each side each square is not one unit but what if each grid square had length of 25 feet okay so I'm gonna write that down this new example what is each grid square what if each grid square has length of 25 feet then I'm going to say find the perimeter what if each grid square has length of 25 feet and I'm going to look at that same rectangle so it was 3 by 4 so I'm gonna draw it right here here's 3 or so it's telling me now that each grid square here's one grid square has length of 25 feet so what that's telling me is that this is 25 this is 25 25 25 25 25 so 25 each of these represents 25 feet not just one unit it's changing the scale of the grid square each grid square is 25 feet so this side would now be 4 times 25 feet which is hundred this side here would be 3 1 2 3 times 25 3 times 25 which is 75 feet and then would find the perimeter well if this is 75 feet so is this and if this is hundred feet so is this and the perimeter is the fence all the way around so would add 100 plus 75 plus 100 plus 75 100 and 100 is 270 and 75 is 150 putting two hundred and 150 together would have fence that is three hundred and fifty feet so again part of your practice today will be plotting ordered pairs and creating polygon and doing what it says like finding the perimeter and you might be changing the the grid Square to different amount like each grid square represents each side of the grid square is 25 feet or some other number all right before the next example the hidden treasure for today so the hidden treasure is being able to explain few terms coordinate plane which we've dealt with today and we'll do another one in just second so coordinate plane axis axis and the origin so on the next example will show you that but that will be the hidden treasure being able to explain what's coordinate plane what's it look like what's the x-axis y-axis and origin okay the next example is identify the shape weight from the coordinates and then find the area so two-part question so identify the shape identify the shape and then find the area okay and these are the ordered pairs you need to put on the coordinate plane 1 comma 1 1 comma 4 3 comma 4 and 5 comma 1 we're going to put those these ordered pairs on coordinate plane okay so let's make another coordinate plane here so going back to the hidden treasure this is coordinate plane right here it has an x-axis and y-axis this is the y-axis this is the x-axis and I've drawn arrows showing that they keep going they also keep going in this direction remember that there's actually four quadrants quadrant 1 2 3 and 4 so we're not going to be using anything outside of quadrant 1 for these points so the first point that we're going to put on our coordinate plane actually let me number this forgot to do that first point is 1 comma 1 so that is going to be right here 1 4 so I'm going to go over one up 4 3 4 over 3 up 4 and then 5 1 out 2 5 over 5 up 1 so there is our shape so I'm going to connect these dots and there's our shape hopefully you can identify that shape not rectangle it is trapezoid it has one pair of parallel bases this is trapezoid and let's go back and put our 1 comma 1 1 comma 4 3 4 and 5 comma 1 okay so step one core first question identify the shape we've done that we've done that identify the shape after we graphed our ordered pairs on to coordinate plane our shape is trapezoid well second thing we have to do is find the area whenever you're finding the area you should always always start with the formula so flip back to your notes you're gonna write it here just in case you don't have it but hopefully you could go back and find area of trapezoid this is the formula for area of trapezoid the area of trapezoid is base 1 Plus base 2 times the height divided by 2 so what is the height of this trapezoid well I'm going to imagine bird landing right here and bird poop goes straight down how many units is that it's 1 2 3 so the height of that trapezoid is 3 base 1 base 2 this is there's one base there's another count how long the bases are this is 2 units 1 2 this is 1 2 3 4 units and again the height was 3 units now just plug in my information into the formula base one plus base 2 times the height divided by 2 so let's do that to base 1 is to base 2 is 4 2 plus 4 times the height which is 3 over 2 which means divided by 2 parentheses first 2 plus 4 is 6 times 3 is 18 so we've got 18 over 2 we simplify that how many twos go into 18 we've got 9 is our answer 9 units squared super important that we've got our label on there for area always counting squares so here is the area and now we've answered both parts identify the shape it was trapezoid find the area using our trapezoid formula we got an area of 9 units squared so that does it for lesson 5 working with coordinate plane doing what it says graphing the shape or the points that it says to see what shape it makes finding what it says whether its perimeter whether its area using formulas so lot of repeat stuff that you've used from previous lessons okay I'll see you soon for the last lesson in Chapter 9 lesson 6