Classifying quadrilaterals on the coordinate plane

classify quadrilateral ABCD choose the option that best suits the quadrilateral we're gonna pick whether it's a square rhombus rectangle parallelogram trapezoid none of the above and I'm assuming we're gonna pick the most specific one possible because obviously all squares are rhombuses or rhombi i guess it's a not all rhombi are squares all squares are also rectangles all squares rhombi and rectangles are parallelogram so we want to be as specific as possible in picking this so let's see point a is at 1 comma 6 so 1 comma 6 I encourage you to pause this video and actually try this on your own before seeing how I do it but I'll just proceed so that's point a right over there point a point B is that negative 5 comma 2 negative 5 comma 2 that's point B Point C is that set some carbonated water so some air is coming up Point C is that negative 7 comma 8 negative 7 comma 8 so that is Point C right over there and then finally Point D is at 2 comma 11 2 comma 11 and actually that kind of goes off the screen this is 10 11 would be right like this so that would be 2 comma 11 if we were extend this this is 10 and this is 11 right up here to calm 11 so let's see what this quadrilateral looks like you have this line right over here this line right over there that line right over there and then you have this line you have this line like this like this and then you have this like this so right off the bat it's definitely a quadrilateral I have 4 sides but the key question are any of these sides parallel to any of the other sides so just looking at that side CB is clearly not parallel to a is clearly not parallel to a d there you just can look at it now it also looks like CED is not parallel to be a but maybe I just drew it badly maybe they actually are parallel so let's see if we can verify that so the way to tell whether two things are parallel is to actually figure out their slopes so let's first figure out the slope let's figure out our slope of a B or B a so let's figure out our slope here your slope is going to be the change in the change in Y over your change in X and in this case you could think of it as we're starting at the point negative 5 comma 2 and we're ending at the point 1 comma 6 so what's our change in Y our change in Y we go from 2 we're going from 2 all the way to 6 or you could say it's 6 minus 2 our change in Y is 4 what's our change in X well we go from negative 5 negative 5 to 1 so we increased by 6 or another way of thinking about it 1 minus negative 5 well that's going to be equal to 6 so our slope here is 2/3 it's 2 over 3 every time we move 3 in the x-direction we go up 2 in the y-direction move through the x-direction go up 2 in the y-direction now let's think about line CD up here line CD line CD what is our slope our change in Y over change in X is going to be equal to let's see our change in let's figure out our change in X first our change in X we go from we're going from negative 7 comma 8 all the way to 2 comma 11 so our change in X we're going from negative 7 to 2 or we could say 2 minus negative 7 so we go we are increasing by 9 that's our change in X so that's going to be equal to 9 and then our change in Y well it looks like we've gone up we've gone from 8 to 11 so we've gone up 3 or we could say 11 minus 8 notice endpoint - start point end point - start point you have to do that on both on the top and the bottom otherwise you're not going to actually be calculating your change in Y over change in X but you notice our change when we go to our x increases by 9r y increased by 3 so the slope here is equal to 1/3 so these actually have different slopes so none of these lines are parallel to each other so this isn't even a parallelogram this isn't even a trapezoid parallelogram you have to have two pairs of parallel sides trapezoid you have to have one pair of parallel sides this isn't the case for any of these or none of these sides are parallel so we would go we would go with none of the above