Answer
Point C(x,y,z)=C (2,4,6) is closest to the yz-plane.
Point A(x,y,z)=A(-4,0,-1) is closest to the xz-plane
Work Step by Step
Given three points in 3D-System such as A(x,y,z)=A(-4,0,-1), B(x,y,z)=B(3,1,-5) & C(x,y,z)=C(2,4,6).
we will discuss these points in XYZ means 3D-System
Now we divided into two cases:
CASE: I
For yz-plane
The distance from a point to the yz-plane is the absolute value of the x-coordinate of the point. As we know from the given points, point C(2,4,6) has the x-coordinate with the smallest absolute value, So point C(2,4,6) is closest to the yz-plane.
CASE: II
For xz-plane
The distance from a point to the xz-plane is the absolute value of the y-coordinate of the point. As we know from the given points, point A(-4,0,-1) has the y-coordinate with the smallest absolute value, So point A(-4,0,-1) is closest to the xz-plane.
