# How to Find Possible Parallelograms With Three Points

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Finding possible parallelograms with three points is something you can do by examining the coordinates of those points. Find possible parallelograms with three points with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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## Video Transcript

Hello. My name is Walter Unglaub and this is how to find possible parallelograms with three points. So, if we're just given three points, we're assuming that we're also given the coordinates of these three points. And I can write those coordinates down as A having X1, Y1 coordinates; B, I'll call the coordinates X2 and Y2, and C, I'll have X3 and Y3. So, the idea here is, because there are three points and we're just missing one last point, due to the definition of a parallelogram, there's actually going to be three possible parallelograms. And, we can visualize them like this. If we connect points B and C, we have a line of a definite length and orientation. Using that same length and orientation, we can connect one end to point A and then we connect points A and B and C to our fourth point, which I'm going to denote as D sub one. So, this is one possible parallelogram, where these two lengths are equal and they are parallel and the same goes for A, D one and B, C. Another possible parallelogram is, if I have a fourth point up here, where this length, A, C, is equal to this length from B to, let's say, D2 and then the length and orientation of A and D two is equal to C, B. Finally, our third parallelogram will be over here, where I have my fourth point to the right of the line B, C. So, if I make that connection there, I can see for D3, a third parallelogram, so that's one parallelogram is another possible. This is another possible one and, finally, this is the third possible parallelogram. So, if I wanted to calculate what the coordinates for D1 one would be, for example, X4, Y4, I can do so in terms of this given information. So, X4 would actually be equal to X1, the X component of A, minus the difference between the X component in B and C, so, this difference in the X direction. Likewise, for the vertical component of the coordinate of D1, I would have Y3, which is the Y value for C and I would subtract from that the difference between the Y values of B and A, which would be equal to Y2 minus Y1. So, these would simplify then for D1 to X1 minus X2 plus X3 for the X component of the coordinate, comma, Y sub one, minus Y sub two, plus Y sub 3. And that would be the last coordinate for one of the three possible parallelograms. My name is Walter Unglaub and this is how to find possible parallelograms with three points.

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