Question

All the points on the x-axis have
A. x = 0
B. y = 0
C. x = 0, y = 0
D. y = 0, z = 0

Answer 1

Hint: Think of some examples where a point is on the x-axis, another on the y-axis, then on the z-axis, x-y plane, y-z plane and then finally on the x-z plane. You will then get an understanding of which coordinate needs to be 0 for the point to lie on a certain axis or in a certain plane.

Complete step by step solution:
If x = 0, it means that the point can move in both, the y-axis’ direction and the z-axis direction. Therefore, if x = 0, the point can be anywhere on the y-z plane.
If y = 0, it means that the point can move in both, the x-axis’ direction and the z-axis direction. Therefore, if y = 0, the point can be anywhere on the x-z plane.
If x = 0 and y = 0, it means that the point can move only in the z-axis direction.
Therefore, if y = 0, z = 0, the point can be anywhere on the x-axis.
A point on the x-axis has some value of x but the y coordinate and z coordinate of that point will always be 0. If the y coordinate or z coordinate were not 0 then the point would no longer be on the x-axis as it has moved some distance in the y-axis direction or z-axis direction.

Therefore, the correct option is option (D) y = 0, z = 0

Note: Consider the following points: (3,4,0), (2,0,5), (0,1,6), (9,0,0), (0,8,0) and (0,0,7). Check where each of these points lie. You will see that (3,4,0) lies in x-y plane, (2,0,5) lies in the x-z plane, (0,1,6) lies in the y-z plane, (9,0,0) lies on the x-axis, (0,8,0) lies on the y-axis and (0,0,7) lies on the z-axis. This helps us in understanding which coordinate needs to be 0 for a point to lie on a certain axis or in a certain plane.