Introduction to Three Dimensional Geometry

Topics in this chapter

• Three-Dimensional Coordinate System
• Point Coordinates and Octants
• Distance Between Points
• Section Formula and Midpoint
• Projections and Reflections
• Loci in Three-Dimensional Space
• Distance From Coordinate Axes

Cheat sheet

Practice questions

1. Question 1Q-02166E

   The perpendicular distance of the point P(-3, 5, -7) from the xy-plane is:

   1. A.3 units
   2. B.5 units
   3. C.7 units
   4. D.15 units
   See the answer and solution
2. Question 2Q-CA6252

   The distance between the points P(1, -2, 3) and Q(4, 2, -1) is:

   1. A.√17 units
   2. B.√41 units
   3. C.7 units
   4. D.9 units
   See the answer and solution
3. Question 3Q-10E1FE

   The point P divides the line segment joining A(-1, 2, 4) and B(5, -4, -2) internally in the ratio AP:PB = 2:1. The coordinates of P are:

   1. A.(1, -2, 0)
   2. B.(3, -2, 0)
   3. C.(3, 0, 2)
   4. D.(2, -1, 1)
   See the answer and solution
4. Question 4Q-AAD833

   A point P lies in the xz-plane, is 5 units from the xy-plane, and is 3 units from the yz-plane. Find all possible coordinates of P.

   See the answer and solution
5. Question 5Q-077EEA

   The point P(0, -4, 0) lies on the:

   1. A.positive x-axis
   2. B.negative y-axis
   3. C.negative z-axis
   4. D.xy-plane but not on an axis
   See the answer and solution