Main content

## 6th grade

### Course: 6th grade > Unit 9

Lesson 3: 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
- Coordinate plane FAQ

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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(17 votes)
- this is confusing how do you do it with out drawing the thing or do you need to(10 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.(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!(5 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(3 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.(7 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)

- Can we use systems of equations to solve this with a parallelogram?(4 votes)
- Is there a way to do this in your head without drawing the coordinate plane?(3 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….(4 votes)
- At0:08, what are vertices?(2 votes)
- Vertices are the points where two straight lines meet(3 votes)

- do you get confused of how the numbers are all the same that is confusing? but cool!(3 votes)

## Video transcript

- [Voiceover] You are graphing rectangle ABCD in the coordinate plane. The following are three of
the vertices of the rectangle. They give us the coordinates. What are the coordinates of point D? Alright, well a good place to start, let's just plot these, the three
vertices that they give us. So it looks like they're
on the first quadrant, so I'm going to focus my coordinate
axes on the first quadrant. So that's going to be my y-axis. And let me now, this is
going to be my x-axis. And let's see. The highest x value that I have, I have a two, I have
a five, I have a five, it looks like it goes up to five. So I could say one, two, three, four, and five. So that's five, I can just do one, two, three, four, and five. Let's see, the highest y value, I have one, one, and a six. It goes up to six. So one, two, three, four, five, and six. I can number them. One, two three, four, five, and six. Now let's plot the points. So let's first point A,
which is at two comma one. X equals two, y is equal to one. So that's that point right over there. Now let's plot point B. Point B is at five comma one. So x equals five, y is equal to one. That's right over there. Now let's plot point C. Point C, maybe I need to
find another color here. Point C is at x is equal
to five, y is equal to six. X is equal to five, y is equal to six. So that 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 x coordinate as this point right over here. So this is going to have
the same x coordinate. So it's going to have an x
coordinate, so let me write this. D is going to have an x coordinate of two. And it's going to have
the same y coordinate as this point up here. So it's going to have
a y coordinate of six. Of six. So D is going to be at
the point two comma six. And you see when we do that, we have set up a nice rectangle here. 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. Alright.