9 5 Polygons in the Coordinate Plane

okay guys so we are on workbook page 709 we're going to be talking about polygons in the coordinate plane so for numbers one and two we want to use the coordinates to find the length of each side of the rectangle then find the perimeter so from the point 1 2 to 1 7 the ones didn't change what did change is the 2 and the seven that's distance of five and then for the next points from point one seven to point four seven the sevens didn't change but the one and the four did that's distance of three units from one to four and then for four seven and four two the fours didn't change but the seven and two change distance of 5 units and then from 4 2 back to 1 2 the twos don't change but the 4 is changed and that's distance of 3 units so the rectangle has sides five three five and three those are the side lengths so to find the perimeter you just add them all up five plus five is ten three plus three is six so 10 plus 6 gives perimeter of 16. so number 2 same thing so from 0 0 to 4 0 the zeros didn't change what changed is from zero to four the coordinate that's distance of four and then from four zero to four four the coordinate stayed the same but the y-coordinate moved four units and then you don't even really need to do the other two because the problem told us that these are rectangles and we know that rectangles have two sides the same and two sides the same so this rectangle is actually square because if these two sides are four and four then the other two sides are four and four but we could just check so the four and four here stayed the same but from four to zero that changed by four and then from zero zero those are the same but from this zero to this four that's distance of four so we just add up all the sides to find the perimeter 4 8 12 16. so that has perimeter of 16. okay now we're going to scroll down and we're going to do numbers 6 and 7. so these say graph each figure and classify it then find the area so we don't know what shapes these are going to be till we graph them so first we want to plot the point 3 negative 2. so we start at the origin 3 to the right down 2. so we're going to put point right here that's point then we have 7 negative 2. so 7 to the right down 2. that's point then we have 8 negative 6 8 to the right down 6. that is point then we have 1 negative 6 1 to the right down 6 point so if connect to these we have trapezoid so now that we have trapezoid we have to use the formula for trapezoid so we have base 1 base 2 you add those times the height divided by 2. so let's find the measurements of base 1 is 1 two three four base two is one two three four five six seven now we have to find the height which has to be 90 degrees so one two three four so base one plus base two times the height divided by two so seven plus four is eleven eleven times four is forty-four so we get twenty two so the area of this is twenty-two units squared okay last one number seven we're gonna graph it so is negative three negative four so three left four down then we have negative three positive five so three left five up two five and then two negative four so now we connect these and it is rectangle we forgot to classify this one let's just write trapezoid so now we want to find the area so we just do base times height or length times width so we have one two three four five and then one two three four five six seven eight nine so the area of this is nine times five so 45 units squared