Polygons on the Coordinate Plane 6 th

we're working on polygons on the coordinate plane and if you want to follow along to this problem it's on page 707 in your workbook it's got it problem see on example three so again page 707 example three got it problems see and here's what it's asking us the coordinates of the vertices of garden are 0 1 0 4 8 4 and 8 1 if each unit represents 12 inches find the perimeter and inches of the garden so let's go ahead and take our coordinates and let's rewrite them down here so we have 0 1 0 4 8 4 and 8 1 and I'm gonna go ahead and give these coordinates name want to give them point name so 4 0 1 let's give it 0 4 let's give it be 8 for and 8 1 of course let's make it and we're trying to find the perimeter so we're looking at the outside measurement the length of those measurements to find out what the perimeter is in this case we have 1 2 3 4 coordinates that create point that we're going to connect if we connect those and we have 4 that means we're gonna have quadrilateral so we need to have 4 sides so let's go ahead and determine what sides we're going to have here well we know we're gonna have line so let's write line is gonna connect to so we're gonna have line BC is going to connect to so we're gonna have line and then we're all dead is gonna connect back to so we'll have line and we need to find the distance of these lines so that we can add them up and get our perimeter and the rule for the coordinates on when you're trying to find out perimeter is that if your x-coordinates are the same you're going to find the difference between the y-coordinate if your y-coordinates are the same you're going to find the difference between your x-coordinate so let's go ahead and mark these out let's see we know our first coordinate is an and our second is the so I'm gonna go ahead and just label these so that we can use them as reference all right so let's go ahead and start filling in what the difference is here so for line it looks like our coordinates are the same so it's 2 so they're the same we're going to do the difference of our coordinates now we do not want any negative numbers on this because we're trying to find the distance and the distance is always positive so don't want to do 1 subtract 4 want to do 4 subtract 1 so that can make sure get positive number so let's go ahead and do that we'll have 4 minus 1 which gives us 3 okay and then we'll do the same for all of our other lines we have line BC for this one our coordinates are the same so we want to find the difference between our coordinates again we do not want negative number so let's do 8 minus 0 to get 8 CD our coordinates are the same so let's find the difference between our coordinates we have 4 minus 1 which gives us 3 and now we have the our coordinates are the same so let's find the difference of our coordinates minus 0 equals 8 and since it's the parameter again we're going to add up the lengths of all of the sides to get what our perimeter is so let's add up the links that we have we have 3 plus 8 plus 3 plus 8 3 plus 8 gives us 11 3 plus 8 gives another 11 11 plus 11 gives us 22 now 22 is not the actual perimeter of this quadrilateral because this is how many units there are when we go back to the problem it tells us each unit represents 12 and it inches so of these 22 units we have to make sure we multiply that by 12 inches so that we have 22 units worth of 12 inches so we'll have 22 times 12 2 times 2 gives us 4 2 times 2 gives us 4 add 0 4 place value 1 times 2 gives us 2 1 times 2 gives us to add it all up and we get 264 go back to make sure you have the correct units in this case we are in inches so therefore the perimeter of these coordinates end up being 264 inches