Optimizing Coverage: Security Cameras (MATH SHELL)

A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. The camera can turn right round through 360° in all directions. The shop owner places the camera at point (6,4), in the corner of the shop. The plan view below shows where ten people are standing in the shop. Drag point P to change the camera location.

1. Which people cannot be seen if camera p is located at (6,4)?

2. The shopkeeper says that “15% of the shop is hidden from the camera.” Show clearly that he is right.

3. Show the best location for the camera, so that the camera can see as much of the shop as possible. Explain how you know that this is the best location for the camera.