Math Help - 3D Coordinate Systems

1. 3D Coordinate Systems

Find the distance from (3,7,-5) to each of the following:

a)xy-plane
b)xz-plane

Can someone explain to me how this is done? there are parts c-f to all different planes and I want to see how it is done to a) and b) thanks.

2) Find an equation of a sphere if one of its diameters has endpoints (2,1,4) and (4,3,10).

2. use the distance formula for a) and b)
Originally Posted by xfyz
Find the distance from (3,7,-5) to each of the following:

a)xy-plane
find the distance between (3,7,-5) and (3,7,0)

we eliminated the z-component for the quickest way to the xy-plane

b)xz-plane
find the distance between (3,7,-5) and (3,0,-5)

we eliminated the y-component for the quickest way to the xz-plane

2) Find an equation of a sphere if one of its diameters has endpoints (2,1,4) and (4,3,10).
use the midpoint formula for the two points. this will give you the center of the sphere. use the distance formula for the distance between the two points. half this distance is the radius

then you know the equation of a sphere: $(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2$

where $(a,b,c)$ is the center and $r$ is the radius