9 4 Polygons in the Coordinate Plane

all right this one is quite doozy we're gonna deal with polygons in the coordinate plane so being able to find lengths of sides and basically using coordinate plane to find area and perimeter of shapes all right here is your warm-up for today give examples of points in each quadrant so want you to give any an example of first quadrant second quadrant third quadrant and fourth quadrant answer come back when you're done so you could have had any numbers put in here for these ordered pairs but this is how it should have been labeled the and would be positive for the first quadrant so three and seven the second quadrant had to be negative and plus so like negative 2 5 third quadrant are both negative so negative 2 negative 6 and 4 4 would be positive and ghost like five and then negative so as long as you had those you did well so here are couple examples you could have based on using that same pattern all right so let's talk about polygons in the coordinate plane first you got to remember what polygon is and that is shape with vertices and straight lines that are equal guess ok on map you can identify location by the intersection of two streets so you can think of coordinate plane as bunch of streets in city well you can also count along the axis to determine distances in plane so here's one where you were given and and the coordinates for it and then this is what it looks like when it is labeled on the coordinate plane that's we're gonna work on today so let's get into our first example which is drawing polygon in the coordinate plane make sure you have that written down drawing polygons and the coordinate plane now if you're given the vertices of few and and you plotted them on coordinate plane like you're supposed to do here you then connect the dots know you guys have played connect the dots before so for you go over 2 and up 5 for you go over 4 and up 1 for hu don't go up or down at all but you go down to not 20 to negative 2 so you graph the points and the second step to doing this is you connect the dots so you just draw lines that go through them so that's the triangle that you would get for example one have this down before moving on here's another example to look at so was given one two for 4 comma 2 for and 3 comma 1 for what do with my drawing is just made the first quadrant and you can see that if you place these on there this is what it would look like graph the dots and then connect the dots all right you have two of them want you do in your notes these are the two shapes want you to create so there's your there are your coordinates and our ordered pairs go ahead and put it on the graph and hear what my to look like based on the coordinate plane that created long skinny rectangle for number 1 and wide rectangle for number 2 hopefully yours look pretty similar all right for practice - we're going to talk about how you can find the distance in coordinate plane first we got to see if we can find the perimeter of this shape now remember perimeter is walking the fence around the outside so how much space takes up just the outside so the first thing you'd have to do in these steps and encourage you to write these down step one is find the length and the width so we got to be able to find the length and width of the shape that we see here now to find that all we have to do is count from left to right along the x-axis from one coordinate to the other and then to find the length going up you do the same thing so if we were able to look at the width let's start at and go to 1 2 3 4 so the width of this is 4 and the height is 1 2 3 4 5 six so six and four are the numbers we need to know now to find the area of rectangle what you have to do make sure you're ready to move on is you have to find the perimeter by using the formula which is 2l plus 2w which means we're multiplying times 2 and our length was I'm sorry 4 and our width was 6 guess it really doesn't matter which direction but to solve this you use this formula 2l plus 2w so what are we gonna do we're gonna plug and chug plug in 4 for so it's now 2 times 4 plus 6 for 2 times 6 order of operations 2 times 4 and 2 times 6 separately and when you add those together you get 20 oops thought had this here for you guess not so for this one would equal 20 here won't let me get rid of the 4 & 6 here are two rectangles want you to find the perimeter of each come back when you figured it out all right so hopefully number 4 didn't trick you up too much but the width of that one was 5 and half she had to add that extra half on there for each of those so there's the formulas used showing my work if perimeter for 3 is 18 and the perimeter for 4 is 21 and let's look at word problem here so it says Candace's house is at the corner of 3rd Avenue and 7th Street she walks from her house west to - 2nd Avenue then south to 4th Street then east to 3rd Avenue and then back home how far did she walk so you got to be able to create your perimeter so the first thing we're gonna do we're gonna plot the points on coordinate plane find the length and the width of the rectangle and then figure out the perimeter so first thing we have to do is make coordinate plane now we know it says that she's she lives at the corner of 3rd Avenue and 7th so if we go over 3 and up seven this is where we're gonna start now she walks from her house west to - 2nd Street so - 2 would be two to the left of the access so how far did she walk here well 1 2 3 4 5 so she walks five blocks that way then it says she went south so we're going down to 4th Street we're at 7th so we got to go down to 4th 6 5 4 so that's difference of three and then back home ok so she went no I'm sorry then we have to go east the third Avenue 3rd Avenue would be about here so how far did we go 1 2 3 4 5 then she went back home and that's the same as over there which is 3 so how far did she walk we just have to add all four numbers up 5 and 5 make 10 3 & 3 makes 6 6 plus 10 is 16 so Candice walked 16 blocks to be able to find that answer so it's okay to draw and kind of think it out even if you're cording to play and look sloppy like mine it's plan which is what you need when trying to deal with word problems here's what want you to try on your own come back when you are done so hopefully you got 22 feet for the perimeter well showed my work here which hope you did in your notebook as well so by putting the string around the border we saw that from negative 2 comma 3 all the way over to 5 comma 3 that's difference of 7 and then 4 going down from 5 3 to 5 negative 1 that was difference of 4 and over then to finish off rectangle so 7 + 4 2 times 7 is 14 2 times 4 is 8 when you add those together you get 22 feet all right go ahead and answer these two word problems or thoughts box of thoughts full sentences these probably both take at least two sentences to solve I'll be looking for good answers inside box when you come to me later and here is your quiz so it's gonna be in three parts so we're gonna pause it as we go first thing you have to do here is graph the rectangle with vertices so make coordinate plane and then graph it when you're done move on to the next one number two you got to find the perimeter of this rectangle and number three albert's set up vegetable garden using coordinate system want you to be able to tell me what the perimeter of the garden is that's it for this lesson we'll see you next time