Question

Daнo A (2; 3; 1), B(-1; 4; 1): D(2;1;1) знайти координати вершини​

Answer 1

Ответ:

Відповідь: - координати вершини C паралелограма (-4;6;1),

- координати точки перетину його діагоналей О (-1;1;1).

Answer 2

To find the coordinates of the vertex, we can use the midpoint formula. The vertex of a triangle is the point where the medians intersect.

Let's find the midpoint of line segment AB, which connects points A and B: Midpoint of AB = ((x_A + x_B)/2, (y_A + y_B)/2, (z_A + z_B)/2) = ((2 + (-1))/2, (3 + 4)/2, (1 + 1)/2) = (1/2, 7/2, 1)

Now, let's find the midpoint of line segment AD, which connects points A and D: Midpoint of AD = ((x_A + x_D)/2, (y_A + y_D)/2, (z_A + z_D)/2) = ((2 + 2)/2, (3 + 1)/2, (1 + 1)/2) = (4/2, 4/2, 2/2) = (2, 2, 1)

Finally, let's find the midpoint of line segment BD, which connects points B and D: Midpoint of BD = ((x_B + x_D)/2, (y_B + y_D)/2, (z_B + z_D)/2) = ((-1 + 2)/2, (4 + 1)/2, (1 + 1)/2) = (1/2, 5/2, 1)

The coordinates of the vertex are (1/2, 7/2, 1), (2, 2, 1), and (1/2, 5/2, 1).