# Problem 3.1

- Author:
- kelseycowles

## The diagram below shows a flag located in the first quadrant. Notice the labels on key points.

## 3.1

A. Copy and complete the table showing the coordinates of points A-D and their images under a reflection in the y-axis.

1. Write the rule relating coordinates of key points and their images after a reflection in the y-axis:
(x, y) --> ( _ , _ )
2. Would your rule give the correct coordinates if the flag started in the second, third, or fourth quadrant? Justify your answers with sketches and samples of coordinates that match.
3. a. Do any points remain unchanged under this reflection? Explain.
b. Do the flag and its image make a symmetric design?

Point | A | B | C | D | |

Original Coordinate | (1.3, 3.89) | (4.07, 2.87) | (2 , 2) | ( _ , _ ) | |

Coordinates After a Reflection | ( _ , _ ) | ( _ , _ ) | ( _ , _ ) | ( _ , _ ) |

## 3.1 Continued

B. Copy and complete the table showing the coordinates of points A-D and their images under a reflection in the x-axis.

1. Write a rule relating coordinates of key points and their images after a reflection in the x-axis:
(x, y) ---> ( _ , _ )
2. Would your rule give the correct coordinates if the flag started in the second, third, or fourth quadrant? Justify your answer with sketches and samples of coordinates that match.
3. a. Do any points remain unchanged under this reflection? Explain.
b. Do the flag and its image make a symmetric design?
C. Copy and complete the table showing coordinates of points A-D and their images under a reflection in the line y=x.

1. Write a rule relating coordinates of key points and their images after a reflection in the line y= x:
( x, y) ---> ( _ , _ ).
2. Would your rule give the correct coordinates if the flag started in the second, third, or fourth quadrant? Justify your answer and give sketches and samples of coordinates that match.

Point | A | B | C | D | |

Original Coordinates | (1.3, 3.8) | (4.0, 2.8) | (_ , _ ) | ( _ , _ ) | |

Coordinates After a Reflection | ( _ , _ ) | ( _ , _ ) | ( _ , _ ) | ( _ , _ ) | |

Point | A | B | C | D | |

Original Coordinates | (1.3 , 3.8) | (4.0, 2.8) | ( _ , _ ) | ( _ , _ ) | |

Coordinates After a Reflection | ( _ , _ ) | ( _ , _) | ( _ , _ ) | ( _ , _ ) | |