What are the coordinates of C in a parallelogram given vertices A, B, and D?

To find C, we can use this property to solve for C. So, if we find the vector from A to B (B - A) and subtract the vector from D to C (C - D), the result should be equal to the vector from A to D (D - A). We can set up an equation and solve for C. In summary, to find the coordinates of point C in parallelogram ABCD, we can use the property that opposite sides are parallel and equal in length. By setting up an equation with vectors, we can solve for C.
  • #1
Delber
19
0

Homework Statement


Given a parallelogram ABCD has vertices A(-1,2,-1), B(2,-1,3) and D(-3,1-3). Find the coordinates of C.

Homework Equations





The Attempt at a Solution


I'm extremely confused here. I do not know how to tell which coordinate is for which vertex on the parallelogram. I know this has to do with vector addition, but I can't picture it to solve the problem.
 
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  • #2
I believe that the convention is that A -> B -> C -> D -> A will traverse the parallelogram. So C is connected by lines to point D and point B. Hopefully that helps
 
  • #3
A, B, C are three points in R^3. Imagine there are three points in your room or wherever. They can be connected to form a triangle. Think about how to turn a triangle into a parallelogram. You can get like three different parallelograms, but the question specifies that the parallelogram is ABCD, not ABDC or ACBD. What this means is described by CrazyIvan.

Opposite sides in a parallelogram are parallel and equal in length. So A - B = D - C.
 

Related to What are the coordinates of C in a parallelogram given vertices A, B, and D?

1. What is the definition of the point of a parallelogram?

The point of a parallelogram is the intersection of its diagonals, where the two diagonals intersect each other.

2. How is the point of a parallelogram calculated?

The point of a parallelogram can be calculated by finding the average of the coordinates of the vertices of the parallelogram. This can be done by adding the x-coordinates of the vertices and dividing by 2, then adding the y-coordinates and dividing by 2.

3. What is the significance of the point of a parallelogram?

The point of a parallelogram is significant because it is the center of the parallelogram and is equidistant from all four vertices. It is also the midpoint of the diagonals, which can be useful in calculating other properties of the parallelogram.

4. How can the point of a parallelogram be used in real life?

The point of a parallelogram can be used in real life in various fields such as architecture, engineering, and design. It is particularly useful in creating symmetrical and balanced structures and designs.

5. Can the point of a parallelogram be located outside of the parallelogram?

No, the point of a parallelogram will always be located within the parallelogram. This is because the diagonals of a parallelogram bisect each other, meaning they intersect at their midpoints, which is the point of the parallelogram.

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