What is the distance from the point (11, -6, -7) to the xz-plane?

Question

What is the distance from the point (11, -6, -7) to the xz-plane?

Answer 1

Hey Jacob,

 

In accordance with WyzAnt's academic honesty policy, I will answer your question generally without specific numbers.

 

Think about what the xz-plane represents. The xz-plane is all of the points in 3-dimensional space for which y = 0.

 

 

Let's assume we're looking for the shortest distance from that point to the xz-plane because there are actually infinite distances from a single point to an entire plane.

 

So how do we find the shortest distance from a point (x1, y1, z1) to the xz-plane? Well since the xz-plane extends forever in all directions with y=0, we actually don't need to worry about the x values or the z values! The shortest distance from a point (x1,y1,z1) to the xz-plane is simply the value of y1.

 

Real life scenario:

Imagine the xz-plane is the floor of your room (i.e. y=0). You are facing the x-direction. The z-direction is to your left and right. How high above the floor is your head? Ok now walk forward... how high is your head now? the same! now walk to the left. your head is still at the same height. the height of your head above the ground is the y-coordinate in reference to the xz-plane (the floor).

 

I hope this helps!

Nic