Polygons on the coordinate plane
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- [Voiceover] Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle, and they give us the labels for the vertices as well. Given these coordinates, what is the length of side AD of this rectangle? So let's just plot it. That's one way that we could tackle it. So let's, let me see, all of these are actually in the first coordinate, so I could focus on the first coordinate. So let's say that's my y-axis. It's my y-axis, and let me draw my x-axis. My x-axis, and actually I wanna really focus in on the points A and D, because we just need to find the length of the side from point A to point D. So point A, let me do this in another color. So point A is at x equals seven, y is equal to one. So one, two, three, four, five, six, seven, so that's x equals seven. Y is equal to one. Y is equal to one, so that is point A right over there. Point A, let me label it. Point A. And then where's point D? Point D has the exact same x-coordinate, but its y-coordinate is a little bit higher. Its y-coordinate is six. It's actually five higher. So point D is at x equals seven, y is equal to six. So y is equal to one, two, three, four, five, and six. So that's y is equal to six, and so we can draw the point. It is going to be right over here. This is point D, and we could actually connect them with a line, if we like, to show that this is a side of a rectangle. Let me draw that. I can just draw this like this. And there you have it. I haven't even drawn the whole rectangle yet, but just by plotting these two points, we can think about how long side AD is. We could say, look, the x doesn't change going from A to D, but we do increase in the y direction by five. We go from y is equal to one to y is equal to five, to y is equal to six. So our change in y is equal to five. So what's the length of this line? Well, it's gonna be five. It's gonna be five, whatever the units are. So that's the length of side AD. It's going to be equal to five. We went from the point (7, 1) to the point (7, 6). Now, they said that this was a rectangle. Now, just for our satisfaction, we can draw the entire rectangle. We have that point B that is at x equals five, y is equal to one, so let me draw that. And I'm just doing this just for fun now at this point. We're done with the problem. So x equals five, y equals one. That's right over here. That's point B. Let me write B. That's the point (5, 1). And then we have the point C. I'll do this in another color. The point C is at x equals five, y equals six. X equals five, y equals six. Point C is right over here. Point C is the point x equals five, y is equal to six. And then we could connect all the dots, if we like, and clearly see that it is a rectangle. So I could connect those. I could connect these two. Then I could connect these two. And then we see that we indeed have a rectangle. But we answered it awhile ago that the length of side AD is equal to five. If we cared about the other sides, the length of BA, well, this is two. a difference of two along the x direction, the horizontal direction, difference of two along the x direction, difference of five in the y direction. We go from y equals one to y equals six. So there you have it. We actually will figure out all of the dimensions of this rectangle.