About this video
The video uses a rectangle on the coordinate plane where the unknown coordinates are labelled with the letters X, Y and Z. Using the fact that corners on the same vertical line share x-coordinates and corners on the same horizontal line share y-coordinates, it finds Y = 4, Z = 3 and X = 2, then sorts them from least to greatest: X, Z, Y.
You'll be able to
- use a rectangle's shape to find a missing coordinate.
- explain that points on a vertical line share x-coordinates and points on a horizontal line share y-coordinates.
- sort values found from a graph from least to greatest.
Key words
- variable
- A letter that stands for a number we don't know yet.
- vertical line
- A straight up-and-down line; every point on it has the same x-coordinate.
- horizontal line
- A straight side-to-side line; every point on it has the same y-coordinate.
Transcript
- [Tutor] So I have copy 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 what Y, Z, and X are and then we need to sort them.
Let's look at Y. And this is a little bit counterintuitive because they're using the variable Y 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 is gonna be the same as the X-coordinate of this point.
They sit on the same vertical line, the way that it's 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 the variable Y for the X-coordinate, which is a little strange, but this is going to be the point (4,7).
So Y is equal to four. Now let's see what we could 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 gonna be at the same level, I guess you could say in the vertical direction.
It's gonna sit on the same horizontal line. So it's gonna have the same Y-coordinate as this point. Now this point has a Y-coordinate of three, so this point's Y-coordinate needs 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 just in another color. X is the X-coordinate for this point. Well, this X-coordinate is gonna 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 is also the variable X, so this is going to be two. If we wanna 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.
It'd be X, then Z, then Y. Two, then three, then four. So actually lemme 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 could check our answer and we got it right.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.