# Precalculus : Reflections

## Example Questions

### Example Question #1 : Reflections

Reflect  across , and then across . What is the equation of the line after the reflections?

Explanation:

The distance between the lines  and  is 6 units. Therefore, the first reflection should be 6 units below .  Therefore, the first reflection is:

The distance between  and  is 7 units.  Therefore, second reflection should be 7 units above .

The result is .

### Example Question #1 : Reflections

Reflect  across .  Reflect again across .  What is the equation of the line after both reflections?

Explanation:

The result of reflecting  across  will become .  Reflecting the equation  across  will become .

The correct answer is .

### Example Question #3 : Reflections

If  was reflected across , then reflected across , and then reflected again across , what is the equation after the three reflections?

Explanation:

First, if  was reflected across , the new line will be .

Reflecting this line  across  will yield .

Reflecting  across  will yield .

The answer is .

### Example Question #4 : Reflections

Which of these functions has been shifted one unit to the right, three units down, and reflected across the -axis?