EasyMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Introduction to Three-Dimensional GeometryNumerical
A classroom is a rectangular room. A teacher takes the corner of the floor where two walls meet as…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A classroom is a rectangular room. A teacher takes the corner of the floor where two walls meet as the origin. The -axis runs along the bottom of the front wall, the -axis runs along the bottom of the side wall, and the -axis runs up the corner. All distances are in metres. A fly rests at the point . Find the height of the fly above the floor. Then find the distance of the fly from the wall that holds the -axis and the -axis.
Need a reminder? The key ideaShow
The three signs of decide the octant. A point on an axis has two zero coordinates, and a point in a coordinate plane has one. The distance of from the -plane is , from the -plane and from the -plane .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. The fly is at m.
Plan. A distance from a coordinate plane is the absolute value of the coordinate that points away from it.
Step 1. The floor. The floor is the -plane. The distance from it is .
Step 2. The wall. The wall that holds the -axis and the -axis is the -plane. The distance from it is .
Check. All three coordinates are positive, so the fly is in the first octant, inside the room.
Answer: the fly is above the floor and from the wall.
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