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 determine the coordinates of point C, you can use the fact that the figure given is a parallelepiped. A parallelepiped is a three-dimensional figure with six quadrilateral faces, where opposite faces are congruent and parallel.
In this case, we can observe that points A, B, C, and D form a quadrilateral face of the parallelepiped. Given the coordinates of points A, B, D, and E, we can infer the coordinates of point C using the property of parallelepiped faces.
Here's how you can determine the coordinates of point C:
1. Start by visualizing the shape of the parallelepiped in your mind or draw it on paper. Mark the known points A, B, D, and E.
2. Since you know the coordinates for A, B, D, and E, you can determine the direction of the missing side. In this case, you can see that point C shares the same y-coordinate as point D (4), but its x-coordinate is the same as point B (3). Point C's z-coordinate remains the same as the other points (2).
3. Based on the information above, you can conclude that point C has the coordinates (3,4,2). Therefore, your determination is correct.
So, by considering the properties of parallelepiped faces and using the known coordinates of other points, you can calculate the coordinates of point C.