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Coordinates of rectangle example

Sal solves a challenging problem involving a quadrilateral on the coordinate plane.

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Video transcript

- [Voiceover] So I've copied and pasted this question from the exercises on Khan Academy. It says, "Sort the following expressions "from least to greatest based on the coordinates "of the rectangle below." So we need to figure out would y, z and x are. Then we assort them. So let's first look at, well let's look at y. And this is a little bit counter intuitive because they're using the variable y to represent the x-coordinate, to represent the x coordinate of this point. So let's see if we can figure out what the x-coordinate of this point is. Well it's a rectangle. The x-coordinate of this point right over here, it's going to be the same as the x-coordinate of this point. They sit on the same vertical line the way that it is drawn. So if this has an x-coordinate of x equals four, then this is going to have an x-coordinate of four. And now we use a variable y for the x-coordinate which is a little strange but this is going to be the point four comma seven. So y is equal to four. Now let's see what we can figure out about z. Well, z is the y coordinate for, let me use another color here, z is the y coordinate for this point. Now, what other point has the same y-coordinate? Well, it's going to be at the same level, I guess you could say, in the vertical direction. It's going to sit on the same horizontal line. So it's going to have the same y-coordinate as this point. Now this point has a y-coordinate of three. So this point, it's y-coordinate is going to be three or we could say that z is equal to three. So this is going to be equal to three. And then last but not least, we need to figure out what x is. And x is the x-coordinate. Let me do this in another color. X is the x-coordinate for this point. Well, this x-coordinate is going to be the same thing as the x-coordinate for this point up here which is equal to two. They sit on the same vertical line. They both sit on the line, x equals two. And so x is going to be two. It is the x-coordinate and it's also the variable x. So this is going to be two. So if we want to sort them from least to greatest, x is the least. Then we would go, it's actually the exact opposite of what we have here. The x then z, then y. Two then three, then four. So actually, let me get the exercise out and just check our answer. So x is the least then z is in the middle and then y is the largest. We can check our answer. We got it right.