1. Minh asks Marco to duplicate a graphic she has on her restaurant’s ceiling. The ceiling is covered with 1 ft by 1 ft tiles. A chandelier hangs in the center of the ceiling. The graphic Minh painted on the ceiling is a pentagon. Assuming that the chandelier is located at , the pentagon’s coordinates are . Minh wants to have the same graphic design duplicated in another location on the ceiling. She is considering four ideas.
(a) reflecting pentagon over the y-axis
a. Graph new pentagon when pentagon is reflected over the y-axis. What are the coordinates of pentagon ?
b. Write a math rule or explanation using words that describe a reflection of over the y-axis.
c. Using this rule, where would be located if reflected over the y-axis?

(b) rotating pentagon 90° clockwise about the origin
a. Graph the new pentagon when pentagon is rotated 90° clockwise about the origin. What are the coordinates of pentagon ?
b. Write a math rule or explanation using words that describe a rotation of 90° clockwise about the origin.
c. Using this rule, where would be located if rotated 90° clockwise about the origin?

(c) translating pentagon to the right 11 units and up 4 units
a. Graph the new pentagon PQRST when pentagon is translated 11 units to the right and 4 units up. What are the coordinates of PQRST?
b. Write a math rule or explanation using words that describe a translation of 11 units to the right and 4 units up.
c. Using this rule, where would be located if translated 11 units to the right and 4 units up?

(d) translating pentagon 3 units up and then reflecting it over the x-axis
a. Graph the new pentagon when pentagon is translated 3 units up and reflected over the x-axis. What are the coordinates of pentagon ?
b. Write a math rule or explanation using words that describe a translation of 3 units up and reflection over the x-axis.
c. Using this rule, where would be located if translated 3 units up and reflected over the x-axis?

2. The restaurant floor, like the ceiling, is made of tiles that measure 1 ft by 1 ft. On the floor, Marco has made this graphic.
For each pair of graphics listed below, decide whether the pair is best described as similar, congruent, or neither. If the pair is similar or congruent, describe the sequence of transformations that proves this and write the congruency or similarity statements for each pair of corresponding sides. If the graphics are neither similar nor congruent, explain how you know this.
(a) polygon and polygon
(b) polygon IJK and polygon LMN
(c) polygon and polygon
(d) polygon and polygon


3. Minh wants to add another graphic on the ceiling. She has a pentagon located at . To make the other pentagon, Minh wants to reflect pentagon over the y-axis. Next, she wants to dilate it by a factor of 2, using the origin as the center of the dilation. Finally, she wants to translate it 15 units down and 2 units right to get the location of the final graphic. What is the location of the new graphic? Show your work.