If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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?

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.