Unit 5: Three Dimensional Coordinates — Online MCQ Test
MATHEMATICS - 1B · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board
Practice Unit 5: Three Dimensional Coordinates with a free chapter-wise online MCQ test.
This chapter covers: Introducing 3D coordinate geometry this chapter covers octants distance between two points in 3D space and section formulas for internal and external division..
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Unit 5: Three Dimensional Coordinates — Important Questions & Answers
How many octants are there in three-dimensional coordinate geometry?
- A. 4
- B. 6
- C. 8
- D. 12
Answer: C. 8
The three coordinate planes divide space into 8 regions called octants.
The three coordinate planes divide space into 8 regions called octants.
Which point lies in the first octant?
- A. (2, 3, 4)
- B. (-2, 3, 4)
- C. (2, -3, 4)
- D. (2, 3, -4)
Answer: A. (2, 3, 4)
In the first octant, all three coordinates are positive.
In the first octant, all three coordinates are positive.
Which point divides the segment joining A(0, 0, 0) and B(6, 0, 0) internally in the ratio 1:2?
- A. (2, 0, 0)
- B. (3, 0, 0)
- C. (4, 0, 0)
- D. (1, 0, 0)
Answer: A. (2, 0, 0)
Using the internal division formula, x = (1·6 + 2·0)/(1+2) = 2, and y and z remain 0.
Using the internal division formula, x = (1·6 + 2·0)/(1+2) = 2, and y and z remain 0.
Which statement is NOT correct about octants in 3D space?
- A. Each octant is bounded by coordinate planes.
- B. There are 8 octants in total.
- C. A point with all coordinates positive lies in the first octant.
- D. A point on a coordinate axis belongs to exactly one octant.
Answer: D. A point on a coordinate axis belongs to exactly one octant.
A point on an axis lies on the boundary of coordinate planes and does not belong to any octant in the strict sense.
A point on an axis lies on the boundary of coordinate planes and does not belong to any octant in the strict sense.
For points A(1, 2, 3) and B(5, 6, 7), which of the following is the midpoint of AB and also the point dividing AB internally in the ratio 1:1?
- A. (2, 3, 4)
- B. (3, 4, 5)
- C. (4, 5, 6)
- D. (6, 7, 8)
Answer: B. (3, 4, 5)
The midpoint is obtained by averaging corresponding coordinates: ((1+5)/2, (2+6)/2, (3+7)/2) = (3, 4, 5).
The midpoint is obtained by averaging corresponding coordinates: ((1+5)/2, (2+6)/2, (3+7)/2) = (3, 4, 5).