The mid-points of the sides of a triangle are `(1,5,-1),(0,4,-2)a n d(2,3,4)dot` Find its vertices.

Explanation

To find the vertices of the triangle given the midpoints of its sides, we can use the properties of midpoints in 3D coordinate geometry. Let's denote the vertices of the triangle as \( A(X_1, Y_1, Z_1) \), \( B(X_2, Y_2, Z_2) \), and \( C(X_3, Y_3, Z_3) \). The midpoints of the sides are given as follows:

- Midpoint \( D \) of side \( AB \) is \( (1, 5, -1) \)
- Midpoint \( E \) of side \( BC \) is \( (0, 4, -2) \)
- Midpoint \( F \) of side \( CA \) is \( (2, 3, 4) \)

### Step 1: Set up the equations for midpoints
Using the midpoint formula, we can set up the following equations:
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