The 3D Coordinate System Examples

Draw a cylinder in the 3D coordinate plane with a radius of 3 units, a height of 7 units, and the center of one of its circular bases at (3, 3, 0).

First, we need to figure out where our base is. A circular base with a center at (3, 3, 0) would look like this on the x-y plane.

Extended 7 units down the z-axis, the cylinder would look like this.

Hopefully your drawing looks more or less like that.

Find the distance between points J (1, 7, -4) and K (7, 2, -10).

The formula for distance in 3D space looks a lot like the distance formula for 2D space.

That's all it takes. JK is 9.8 units. No, we aren't JK-ing.

You're flying a Pikachu kite while standing at the point (0, 0, 0). The kite is at the point (9, 8, 12) when it runs out of string. If one unit is equal to 22.6 inches, how long is the string?

The first order of business is to find the distance (in units) between you and the kite. That's the length of the string.

d = 17 units

The string is 17 units long. That doesn't really help us. We should get it into actual measurements, like inches.

d = 17 units × 22.6 inches/unit = 384.2 inches.

That's about 32 feet.

Find the center and radius of a sphere with a diameter whose endpoints are at (2, -3, 7) and (6, 4, 3).

The diameter of a sphere passes through the center. Actually, the center of the sphere is the exact midpoint of the diameter. Good thing we have a formula for that.

Our center is M. Done. Well partially, anyway.

To find the radius, we can either cut the diameter in half or find the distance between the center and one of the diameter's endpoints. Chopping things up is always fun, so let's do that.

d = 9

That's our diameter. To cut it in half (sans butcher knife), we divide by 2.

r = 4.5

Our sphere has a center M (4, ½, 5) and a radius of 4.5.