I have this number that I just wanted to be sure how to do. They give me a Parallelepiped with corners lettered from A to H. Then the question is:

In a certain orthonormal reference, the coordinates of points A, B, D and E are respectively

A(0,0,2)
B(3,0,2)
D(0,4,2)
E(0,0,1)

Calculate the coordinates of point C in that same reference.

I determined that the coordinates for C are (3,4,2) but I have no idea how one goes to calculate that. I'm looking for a method to resolve this number.

Thank you

To find the coordinates of point C, you can use the fact that the opposite corners of a parallelepiped have equal x, y, and z coordinates.

Let's examine the given points:

A(0,0,2)
B(3,0,2)
D(0,4,2)
E(0,0,1)

From points A and B, we can deduce that along the x-axis (horizontal), the coordinates remain the same, i.e., x is constant.

Similarly, from points A and D, we can conclude that along the y-axis (vertical), the coordinates remain the same, i.e., y is constant.

Now, let's determine the coordinates of point C.

Along the x-axis, we observe that the x-coordinate of point C must be the same as point B, which is 3.

Along the y-axis, the y-coordinate of point C should be the same as point D, which is 4.

Finally, for the z-coordinate, we notice that the z-coordinate of point C remains the same as the other points, which is 2.

Thus, the coordinates of point C are (3, 4, 2).

By following this method, you can find the coordinates of other points in a parallelepiped, given some of the coordinates.