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Classifying quadrilaterals on the coordinate plane

Video transcript
Classify quadrilateral ABCD. Choose the option that best suits the quadrilateral. We're going to pick whether it's a square, rhombus, rectangle, parallelogram, trapezoid, none of the above. And I'm assuming we're going to pick the most specific one possible, because obviously all squares are rhombuses, or rhombi, I guess you'd say. Not all rhombi are squares. All squares are also rectangles. All squares, rhombi, and rectangles are parallelograms. So we want to be as specific as possible in picking this. So let's see, point A is at 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 B is at negative 5 comma 2. That's point B. Point C is at-- just had some carbonated water, so some air is coming up. Point C is at negative 7 comma 8. So that is point C right over there. And then finally, point D is at 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 to extend this, this is 10 and this is 11 right up here. 2 comma 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 like this, and then you have this like this. So right off the bat, well it's definitely a quadrilateral. I have four sides. But the key question, are any of these sides parallel to any of the other sides? So just looking at it, side CB is clearly not parallel to AD. You just can look at it. Now it also looks like CD is not parallel to BA, 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 of AB, or BA. So let's figure out our slope here. Your slope is going to be 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 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 2/3. Every time we move 3 in the x direction, we go up 2 in the y direction. Move 3 in the x direction, go up 2 in the y direction. Now let's think about line CD up here. 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'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 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 minus start point. Endpoint minus start point. You have to do that 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 our x increases by 9, our 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 with none of the above.