 Light Bounce

• ## Light Bounce

This tool allows you to investigate the new Light It Up game at the Springfield Fair. The game involves aiming a laser pointer from a height of 150 units at a mirror (M) that is 10 units off the ground and 25 units from the wall.
The goal is to make the reflection of the beam (R) reach a height of exactly 1,000 units up the wall. The difficulty is determining the proper distance from the wall at which to place the pointer (P).

### Instructions

• Use the three red dots on the screen to adjust the parameters for this investigation. The parameters are:
• The vertical height of the flashlight
• The distance of the mirror from the wall
• The distance of the flashlight (P) from the wall.
Note that the mirror is 10 units off the ground.
• Drag point P back and forth along the horizontal gray line. As P moves, the reflection off of a mirror (M) will reach a point on the wall (R).

### Exploration

• Drag the red dots to adjust the parameters for this investigation so that Distance from Pointer (P) to Floor is 150 units, and the Distance from the Mirror (M) to Wall is 25 units. At what distance (P) should the laser pointer be located so that the reflection (R) reaches a height of exactly 1,000 units?
• In general, what is the relationship between the height of the reflection (R) and the distance from the pointer (P) to the wall?
• Collect data to determine the relationship.
• What algebraic rule can be used to determine the location of the laser pointer when the height of the reflection is known?

### Objectives and Standards

NCTM Standards and Expectations
• Algebra
• High School (9-12)
• Algebra