In order to draw the axes for three dimension, we look at the Cardinal direction and we draw the vertical axis which is called the Z-axis in the North direction. Then we draw the X-axis in the South West direction, the Y-axis in the South East direction,the negative X-axis in the North East direction, and the negative Y-axis in the North West direction. Please click on the image for better understanding.
We would like to plot two points, the point P at coordinates (5,7,3) and the point Q at coordinates (-2,3,4). We are then going to draw a line through these two points.To do so, we go five units along the X-axis and then draw a line parallel to Y-axis that intersect the X-axis at x=5. Please click on the image for better understanding.
We would like to plot the point P at coordinates (5,7,3).We go seven units along the Y-axis and then draw a line parallel to X-axis that intersect the Y-axis at y=7. Please click on the image for better understanding.
We now draw a line from the origin of the axes O, that has coordinate (0,0,0) to the point where both the line X=5 and the line Y=7 intersect. That point R has the coordinate (5,7,0).
We now draw a vertical line from the point (5,7,0) parallel to the Z-axis.
We go to the Z-axis and at z=3, draw a line parallel to the line that connects the point (0,0,0) and (5,7,0). Wherever that line intersects, the vertical line from the point (5,7,0) that is parallel to the Z-axis, that intersection is our desired point, P. Please click on the image for a better understanding.
In order to have a better understanding, we can visualize a point in three dimension as the corner of a box. If we look at the image for this step #5 we see a corner of the box defined by the point P(5,7,3). Please click on the image for better understanding.
Similarly, To plot the point Q at coordinates (-2,3,4), We follow the instructions given in the previous Steps. That is we are going to draw a line at x= -2 parallel to the Y-axis, Then we draw a line at Y=3 parallel to the X-axis the point S where the line X=-2 and the line Y=3 intersect has coordinate (-2,3,0). Please click on the image for better understanding.
Step 7
Now, from the point S(-2,3,0) we draw a vertical line parallel to the Z-axis that is four units in length. The point Q is (-2,3,4). Please click on the image for better understanding.
