Drawing in 3D Rectangular Coordinates z x y

The key to plotting points in rectangular coordinates is to each coordinate as a vector, in the x, y and z direction. z x y

Plotting the point (3,7,5) First, mark off vectors of each coordinate X=3 Y=7 Z=6 Then add your vectors, head to tail starting at your z coordinate Then connect the parallelograms straight up and down

Plotting the point (3,7,6) (continued) Where is your final point? You have to imagine that your "rectangular box" has corners… One of these corners is at the origin (0,0,0) The final point is always on the opposite corner from the origin (0,0,0) Final Point (3,7,6)

Plotting the point (2,-4,3) It really doesn't matter which order you make your rectangular box… Just remember that the final point is always at the corner opposite of the origin

Plotting the point (-4,1,-2) It just usually helps to draw the parallelogram in the x y plane first, then construct the rest of the box

Draw the region bounded by -2<x<2 -3<y<3 -3<z<3

Triangles in 3D What is the distance from origin to the Point (x,y,z) ? Use Pythagorean theorem twice! Length of red line = Length of purple line = =