1. Ch. 10 – 3D Analytic Geometry
10.1 – The 3D Coordinate System

2. The Coordinate System Positive x-direction comes “out of the page”z
Positive x-direction comes “out of the page”
Positive y-direction goes to the right
Positive z-direction goes straight up
xy plane y
xz plane x
yz plane

3. The Coordinate System x y z
Instead of quadrants, we now have octants, designated in the figure by cubes
Octant I has x, y, and z positive (closest to you)
Octants II – IV are counterclockwise around the z-axis
Octants V-VIII are below Octants I – IV, respectively
Octant II
Octant I
Octant V

4. The Coordinate System Plot the following points: (2, 3, 3) (3, -1, 2)x y z
Plot the following points:
(2, 3, 3)
(3, -1, 2)
(1, 4, 0)

5. Distance Formula In 2D, distance formula and midpoint formula are…
In 3D, the formulas change to…
Ex: Find the distance between (4, 1, 1) and (-3, 2, 0). Then find the midpoint of those two points.

6. Spheres In 2D, the general formula for a circle is…
In 3D, the general formula for a sphere is…
Ex: Find the center and radius of the sphere with the equation x2 + y2 + z2 – 2x + 4y – 6z + 8 = 0.
Complete the square!
(h, k) is the center
r is the radius
(h, k, j) is the center
r is the radius
Center = (1, -2, 3)