# How to find the fourth point on a plane defined by 3 points

I am attempting to draw a plane defined by three points.

What I've done is I started out with a vertical rectangle in perspective, and I've drawn three points at varying distances from the points on the vertical rectangle, along the lines connecting the corners to the vanishing point.

Now, however, I am trying to find where the fourth point on the plane, defined by these last three points, should go. According to the picture, the fourth point should be on the line labeled with the question mark--but for the life of me I can't figure out where. Is there a general technique in drawing to find the point?

Homework, I presume.

Lines A,B,C and D are parallel because they meet in a vanishing point on the horizon in your drawing (I cropped it off).

I guess you are not going to draw a rectangular piece. But there's one rectangle, so A and C are as high from the ground. I call the common plane of lines B and D "the ground".

The green line, one of your 2 plane defining lines is continued to the horizon. There must be the vanishing point for all lines which are parallel with the green line. The blue line is one of them. It isn't directly above the green line, it's only parallel with it.

The crossing of A and the blue line is the point you wanted, because the blue line must have same elevation from the ground as A and C.

ADD due a comment: The case is maybe more understandable with the next image which has a little less distorting perspective. The vanishing points unfortunately do not fit into this image:

The questioner is going to draw the green non-rectangular box. It's got from a rectangular box by rotating one plane of a rectangular box around corner X. Other 5 planes are intact. What's taken off from the original box is shown with transparent grey.

• Hello! Thank you for the answer. I was wondering how you knew that the green line and the blue line are parallel. They are on the same plane, but it is not obvious to me that they are parallel. How were you able to deduce that? May 25 '20 at 0:09
• I drew it as parallel with the green line. I connected one of your plane definition points to the point where the green line meets the horizon. That's the vanishing point of all possible lines which are parallel with the green line. May 25 '20 at 0:15
• Hi! Thank you for the edit. It's much clearer now. May 25 '20 at 2:25

Because you have only 2 points of perspective, the verticals (purple lines below) will all be the same angle, merely differing lengths.

Merely copying the vertical angle, will provide last cube point.

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Note that only one purple line was drawn (the frontmost corner), then it was copied and moved.

You have several errors in your project.

Let me start making the horizon horizontal (magenta), and assuming the vertical axis as straight, without vanishing point.

As you can see the cyan lines goes to one perspective point, but the greens on your drawing do not (?)

It is valid to have additional vanishing points, but you do not have that defined.

So assuming that the only vanishing points are the ones marked, you should correct your image as this:

One additional problem is that the green vanishing point is too close to the geometry, so the perscepctive is too forced.