In Class Work

Steps in plotting points on 3D axes drawn in 2D:

By the end of these steps, you will have plotted the desired point, and also have sketched a locator-box that shows any observer where the point is located in space.

To plot the point (X,Y,Z):

1. Draw and label omniscient view of axes
2. Mark a vertex X units along the x axis
3. Draw a dashed vertical line Y units from that point
(up if Y is positive, down if Y is negative).

Connect that point to (0,Y,0) on the y-axis.
This new line segment should be parallel to the x-axis,
not horizontal.

These two lines along with the x-axis and y-axis will
form the left or right side of the locator-box.

4. Go back to the point (X,0,0), and repeat the above
step for the z-coordinate.

That is, draw a dashed horizontal line Z units (X,0,0)
(left if Z is negative, right if Z is positive).

Connect that point to (0,0,Z) on the z-axis.
This new line should again be parallel to the x-axis,
not vertical.

These two lines along with the x-axis and z-axis will
form either the top or bottom of the locator-box.

5. Draw a dashed vertical line from (0,0,Z) up or
down to the point (0,Y,Z).

Connect this new point to the point (0,Y,0) with a
horizontal line.

These two lines along with the y-axis and the z-axis
will form either the front or the back of the locator-box.

6. Now we are finally ready to plot point (X,Y,Z), along
with the last of the dashed lines that together will show
any observer where our point is located in space.

Draw dashed line segments horizontally from point (X,Y,0),
vertically from point (X,0, Z), and parallel to the x-axis
from point (0,Y,Z).

Where these segments intersect is the desired point (X,Y,Z).

If all has gone well, all the dashed lines, along with the axes,
should form a box, showing how far out, up, and over from
the origin our point (X,Y,Z) is.

Voila! We have plotted one 3D point!


  1. Plot the following points, each on its own set of 3D axes.
    1. (-1,0,0)
    2. (0,-2,3)
    3. (1,2,3)
    4. (3,1,-2)
  2. Find the distance between P(-1,0,0) and Q(3,1,-2).


Next!


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