Question

if the cube shown above is sliced by a plane to create a triangle, which sets of vertices could the plane pass through?
a. 1, 3, and 4
2, 3, and 8
1, 3, and 7
b. 4, 5, and 7
1, 2, and 7
2, 3, and 7
c. 3, 5, and 8
1, 2, and 6
2, 4, and 7
d. 4, 5, and 7
1, 3, and 8
2, 4, and 7

Explanation:

Step1: Visualize plane - vertex combinations

A plane passing through 3 non - collinear vertices of a cube can form a triangle. We need to check each option for non - collinear vertices.

Step2: Analyze Option A

Vertices 1, 3, and 4 are non - collinear and can form a triangle. Vertices 2, 3, and 8 are non - collinear and can form a triangle. Vertices 1, 3, and 7 are non - collinear and can form a triangle.

Step3: Analyze Option B

Vertices 4, 5, and 7 are non - collinear and can form a triangle. Vertices 1, 2, and 7 are non - collinear and can form a triangle. Vertices 2, 3, and 7 are non - collinear and can form a triangle.

Step4: Analyze Option C

Vertices 3, 5, and 8 are non - collinear and can form a triangle. Vertices 1, 2, and 6 are non - collinear and can form a triangle. Vertices 2, 4, and 7 are non - collinear and can form a triangle.

Step5: Analyze Option D

Vertices 4, 5, and 7 are non - collinear and can form a triangle. Vertices 1, 3, and 8 are non - collinear and can form a triangle. Vertices 2, 4, and 7 are non - collinear and can form a triangle.

All the sets of vertices in options A, B, C, and D can form triangles when a plane passes through them.

Answer:

A. 1, 3, and 4; 2, 3, and 8; 1, 3, and 7
B. 4, 5, and 7; 1, 2, and 7; 2, 3, and 7
C. 3, 5, and 8; 1, 2, and 6; 2, 4, and 7
D. 4, 5, and 7; 1, 3, and 8; 2, 4, and 7