3D Geometry – Distance Formula, Section Formula, Centroid

Grade 11 Maths — 3D Geometry – Distance Formula, Section Formula, Centroid: 25 practice questions with instant scoring and explanations.

1. The distance between points (1, 2, 3) and (4, 5, 6) is:
2. The distance formula in 3D is:
3. The distance from origin to point (3, 4, 0) is:
4. If P divides segment from A(1, 2, 3) and B(7, 8, 9) in ratio 1:2 internally, P is:
5. The section formula for internal division in ratio m:n is:
6. The midpoint of segment from (1, 3, 5) to (5, 7, 9) is:
7. The centroid of triangle with vertices A(1, 2, 3), B(3, 4, 5), C(5, 6, 7) is:
8. The centroid formula for triangle with vertices (x₁, y₁, z₁), (x₂, y₂, z₂), (x₃, y₃, z₃) is:
9. The distance between (0, 0, 0) and (3, 4, 0) is:
10. If point P divides AB in ratio 2:1 externally where A = (1, 2, 3), B = (4, 5, 6), P is:
11. The centroid of tetrahedron with vertices A, B, C, D is at:
12. Distance of point (1, 2, 3) from origin is:
13. If M is midpoint of AB where A = (2, 4, 6), B = (8, 10, 12), M is:
14. The distance between (1, 0, 0) and (0, 1, 0) is:
15. Point P divides segment from (0, 0, 0) to (8, 4, 12) in ratio 1:3 internally. P is at:
16. The distance from (2, 3, 6) to (2, 3, 8) is:
17. Centroid of triangle with vertices (0, 0, 0), (6, 0, 0), (0, 6, 0) is:
18. If distance from (a, 2, 1) to (1, 2, 3) is 2√2, then a equals:
19. The section formula for external division in ratio m:n is:
20. Distance between (3, 4, 5) and (1, 2, 3) is:
21. If centroid of triangle is (2, 3, 1) and two vertices are (1, 2, 0), (3, 4, 2), third vertex is:
22. The x-coordinate of centroid of (2, 3, 4), (4, 5, 6), (6, 7, 8) is:
23. For points P(a, b, c) and Q(d, e, f), midpoint is:
24. Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²] gives distance between:
25. If distance between two points is 0, then the points are: