Question

В параллелепипеде abcda1b1c1d1 вершины a (1;-4;2) и c (3;-2;8). Определить координаты точки пересечения его диагоналей.

Answer 1

$x= \frac{1+3}{2}=2;y= \frac{-4-2}{2}=-3;z= \frac{2+8}{2}=5;O(2;-3;5).$

Answer 2

Given Information:

We are given a parallelepiped with vertices A(1, -4, 2) and C(3, -2, 8). We need to determine the coordinates of the point of intersection of its diagonals.

Solution:

To find the point of intersection of the diagonals, we need to find the coordinates of the midpoint of the diagonal AC and the midpoint of the diagonal BD. The point of intersection will be the average of these two midpoints.

Let's find the coordinates of the midpoint of diagonal AC first.

The midpoint of a line segment with endpoints (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by the formula:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)

Using this formula, we can find the midpoint of diagonal AC:

Midpoint_AC = ((1 + 3)/2, (-4 + -2)/2, (2 + 8)/2) = (2, -3, 5)

Now, let's find the coordinates of the midpoint of diagonal BD.

To find the coordinates of the midpoint of diagonal BD, we need to know the coordinates of vertices B and D. Unfortunately, the coordinates of vertices B and D are not provided in the given information. Without this information, we cannot determine the coordinates of the midpoint of diagonal BD or the point of intersection of the diagonals.

Therefore, we cannot determine the coordinates of the point of intersection of the diagonals without the coordinates of vertices B and D.

If you have the coordinates of vertices B and D, please provide them, and I will be able to help you further.