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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-11-OCT-01
Coordinate Axes, Planes & Octants — Assignment
Chapter: Introduction to Three-Dimensional Geometry
Topic: Coordinate Axes, Coordinate Planes and Octants
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The number of octants is:
  • A.$4$
  • B.$8$
  • C.$6$
  • D.$2$
2.
The coordinates of the origin are:
  • A.$(0,0,0)$
  • B.$(1,1,1)$
  • C.$(0,0,1)$
  • D.$(1,0,0)$
3.
On the $xy$-plane, the $z$-coordinate is:
  • A.$1$
  • B.$0$
  • C.$-1$
  • D.any value
4.
The point $(2,-3,4)$ has $y$-coordinate:
  • A.$2$
  • B.$-3$
  • C.$4$
  • D.$0$
5.
A point on the $x$-axis has the form:
  • A.$(0,y,0)$
  • B.$(x,0,0)$
  • C.$(0,0,z)$
  • D.$(x,y,0)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
In which octant does $(1,2,3)$ lie?
7.
What is the $z$-coordinate of any point on the $xy$-plane?
8.
Name the plane $z=0$.
9.
Write the general coordinates of a point on the $x$-axis.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write the coordinates of the projection of $(2,3,4)$ on the $xy$-plane.
11.
In which octant does $(-1,-2,-3)$ lie?
12.
Find the reflection of $(2,3,4)$ in the $xy$-plane.
13.
Name the three coordinate planes.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
State the octant of each point: $(1,-2,3),\ (-1,2,-3),\ (-2,-3,-1)$.
15.
Find the image of $P(3,4,5)$ in (i) the $yz$-plane and (ii) the $x$-axis.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $8$
  2. (A) $(0,0,0)$
  3. (B) $0$
  4. (B) $-3$
  5. (B) $(x,0,0)$
Section B — Short Answer (2 marks)
  1. The first octant.
  2. $0$.
  3. The $xy$-plane.
  4. $(x,0,0)$.
Section C — Short Answer (3 marks)
  1. $(2,3,0)$.
  2. The seventh octant.
  3. $(2,3,-4)$.
  4. The $xy$, $yz$ and $zx$ planes.
Section D — Long Answer (5 marks)
  1. IV, VI and VII respectively.
  2. (i) $(-3,4,5)$; (ii) $(3,-4,-5)$.
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