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# Coordinates of rectangle example

Learn how to sort coordinates from least to greatest using a rectangle diagram. Understand how x, y, and z coordinates relate to each other. Discover that y equals four, z equals three, and x equals two. Master sorting these values in ascending order: x, z, y.

## Want to join the conversation?

• This is confusing and counter-intuitive but maybe that's a good thing because it forces you to correctly associate the x/y axes with the 2 values in an ordered pair.
I used a, b and c instead of x, y and z to make this easier to understand.
• very confusing indeed
• why does x go first instead of y
• With a coordinate grid, the horizontal direction, or "axis" is called the x axis. The vertical direction, or axis, is called the y axis. In ordered pairs, the things in parentheses that tell you what point it's referring to, the x axis is always the first number, probably because it's first in the alphabet.
• So is this like a number swapping place to place
• How do you find the length of a shape with coordinates.
• Find the distance between two points. So in this video, we end up with (2, 7) and (2, 3). This distance between 3 and 7 is 4, so we know the side between those two points has a length of 4.
• this video has nothing to do with the quizes and assignments
• It kinda does
• Someone please comment if you don't understand and/or if I'm wrong:

There are two versions of this problem: Rectangle and Parallelograms

Step by step for finding Rectangle coordinates:

1. You first check if the variable is an “X” or “Y” coordinate. For example: In (a, 2), "a" is the X coordinate. In (4, d), "d" is is the Y coordinate.
2. Check the coordinate that is BELOW or ABOVE the variable you're searching for. If there's a rectangle and (a, 2) is ABOVE of the coordinate (10, 5), then a = 10. If (4, d) is BELOW of the coordinate (10, 20) then d = 20.
3. Compare variable values from greatest to least.

Step by step for finding Parallelograms coordinates:

1. Repeat the first step from the RECTANGLE by identifying if the variables are "X" or "Y" coordinates.
2. To find the value of the variable that is a "X" coordinate, you search for the "X" value that is on the DIAGONAL OPPOSITE SIDE. Example: If the variable that is an “X” coordinate is located on the TOP RIGHT of the parallelogram, then the correct coordinate would be on the BOTTOM LEFT.
3. If the variable is a “Y” coordinate like for example (10, d), then you find the “Y” coordinate value that is HORIZONTALLY ON THE OPPOSITE SIDE.
4. Compare variable values from greatest to least.
• what are the digits of pi?
(1 vote)
• Well, pi (π) has infinite non-repeating decimals after the point. So the most common ways to abbreviate are:
- 22/7
- 3.14

Extra digits are: 3.14159265358979323... so on so forth. Most of the time you can just use 3.14.
• THE VERTICES OF A RECTANGLE ARE A(4,6), B(4,-1), C(0,-1)< D(0,6) what are the dimensions of the rectangle?
• In this case the dimensions of the rectangle is 5×7.
(1 vote)
• i'm kind of confused... how do you know which number to substitute for x,y, and z? what is the specific strategy? can someone explain it better? thank you
• To solve equations with three variables, you need to eliminate one variable at a time until you have one equation with one variable left. Then you can solve for that variable and use back-substitution to find the other two variables. You can use elimination by adding or subtracting two equations that have the same coefficient for one variable. You can also use other methods such as matrices or cross multiplication.For example, suppose you have the following system of equations:

x + y + z = 6 2x - y - z = -1 -x + y - z = -4

To eliminate one variable, say z, you can add or subtract two equations that have the same coefficient for z. For example, you can add the first and second equations to get:

3x = 5

Then you can divide both sides by 3 to get:

x = 5/3

Now you have the value of x, and you can substitute it into any of the original equations to find y or z. For example, if you substitute x = 5/3 into the first equation, you get:

5/3 + y + z = 6

Then you can solve for y or z by isolating them on one side. For example, if you solve for y, you get:

y = 6 - 5/3 - z

Now you have an expression for y in terms of z, and you can substitute it into another equation to find z. For example, if you substitute y = 6 - 5/3 - z into the third equation, you get:

-5/3 + (6 - 5/3 - z) - z = -4

Then you can simplify and solve for z by collecting like terms and isolating z on one side. You get:

z = 1/3

Now you have the value of z, and you can substitute it back into the expression for y to get:

y = 6 - 5/3 - 1/3

y = 4/3

So the solution is (x, y, z) = (5/3, 4/3, 1/3).I hope this helps.
(1 vote)

## Video 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.