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### Course: Get ready for Geometry > Unit 2

Lesson 1: Polygons on the coordinate plane- Drawing a quadrilateral on the coordinate plane example
- Drawing polygons with coordinates
- Area of a parallelogram on the coordinate plane
- Area and perimeter on the coordinate plane
- Coordinates of a missing vertex
- Example of shapes on a coordinate plane
- Dimensions of a rectangle from coordinates
- Coordinates of rectangle example
- Quadrilateral problems on the coordinate plane
- Quadrilateral problems on the coordinate plane
- Parallelogram on the coordinate plane

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# Coordinates of a missing vertex

This lesson teaches how to find the missing vertex of a rectangle on a coordinate plane. By understanding that rectangle sides are parallel and vertices form right angles, we can determine that the missing vertex shares its x-coordinate with one vertex and its y-coordinate with another.

## Want to join the conversation?

- Kinda not fair, he gets easy ones while us, we get hard ones(35 votes)
- this is confusing how do you do it with out drawing the thing or do you need to(12 votes)
- I don't understand the question, but I'm gonna assume you mean thinking mentally. A wise teacher once said, "when in doubt, write it out." It's ok not to be able to think of it first inside our heads. Drawing the graph is optional, graph paper is easier to read.(14 votes)

- It's kind of confusing, but after 1,000,000,000,000 tries in the Practice: Area and perimeter on the coordinate plane, I finally get it now.

xd(4 votes)- My estimate if you did 20 tries an hour, you are roughly 3700 years old. Even if you could do 1 try a minute, you would still be 1900 years old. So I guess this is just using the hyperbole of English.(9 votes)

- Hi! I have a question: What exaclty is a vertex? Thanks, 990011389.(5 votes)
- In a (2-dimensional) polygon, a vertex is the intersection of two adjacent sides. Vertices can be thought of as corners.

Note that in any polygon, the number of sides equals the number of vertices.

Have a blessed, wonderful day!(7 votes)

- Is there a way to do this mentally or in our heads, because then we will have to write it out every time. Also it would be much faster….(7 votes)
- Is there a way to do this in your head without drawing the coordinate plane?(5 votes)
- Finally, something my brain can compute(6 votes)
- How can I find the location of D if ABCD is a trapezoid A (_3,5) B (_5,1) C (_1,_1)(2 votes)
- You can't.

A trapezoid is a quadrilateral with one pair of parallel sides, so either 𝐴𝐵 is parallel to 𝐶𝐷, or 𝐴𝐷 is parallel to 𝐵𝐶, but we don't know which it is, and even*if*we knew for example that 𝐴𝐵 is parallel to 𝐶𝐷, we still wouldn't know how long 𝐶𝐷 is.(7 votes)

- Given three of the vertices of a rectangle, can you find the fourth?(3 votes)
- Yes! If you graph your 3 vertices, you should be able to see roughly where the fourth would be located. Mathematically, it would be the same distance as the vertex across the diagonal is from the other two vertices. You can use this distance to find the coordinates.(4 votes)

- Can we use systems of equations to solve this with a parallelogram?(4 votes)

## Video transcript

- [Instructor] You are
graphing Rectangle ABCD in the coordinate plane. The following are three of
the vertices of the rectangle, and they give us the coordinates. What are the coordinates of point D? All right, well, a good place to start. Let's just plot these, the three
vertices that they give us. So it looks like they're
all in the first quadrant. So I'm gonna focus my coordinate
axes on the first quadrant. So that's going to be my y-axis. And let me now, that's gonna be my x-axis. And let's see, the highest x value that I have, we have a 2, I have a 5, I have a 5. It looks like it goes up to 5. So I could say 1, 2, 3, 4, and 5. So that's 5. I can just number them 1, 2, 3, 4, and 5. And let's see the highest
y value of 1, 1, and a 6. It goes up to 6. So 1, 2, 3, 4, 5, and 6. I can number them 1, 2, 3, 4, 5, and 6. Now let's plot the points. So let's first plot point A, which is at 2,1. x equals 2, y is equal to 1. So that's that point right over there. Now let's plot point B. Point B is at 5,1. So x equals 5, y is equal to 1. That's right over there. Now let's plot point C. Point C, and you can find another color here, point C is at x is equal to 5, y is equal to 6. x is equal to 5, y is equal to 6. So it sticks us roughly right over there. And so we need to figure
out what D is going to be. Well, D is going, this is a rectangle, the sides are parallel, all the vertices, we have right angles at all the vertices. So point D is going to have the same, the same x-coordinate as
this point right over here. So it's gonna have the same x-coordinate, and so it's going to have an x-coordinate, so lemme write this, D is gonna have an x-coordinate of 2, and it's gonna have the same y-coordinate as this point up here. So it's gonna have a y-coordinate of 6, of 6. So D is going to be at the point 2,6. And you see when we do that, we have set up a nice, a nice rectangle here. And we can draw the rectangle. So that's one side, that's the top side, that's another side, another side, and then we have that just like that. There you go. We have our rectangle. But most importantly, we
answered our question: What are the coordinates of point D? All right.