Transformations and Congruence Portfolio
Use the worksheet to record your answers to the Transformations and Congruence portfolio activity. Make sure to use correct academic tone and complete sentences when answering the questions. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.
First, do an internet safe search for a video explaining the different transformations of a figure on a coordinate plane. Watch and listen to the presenter in the video, and apply what you learned to your portfolio.
This portfolio includes a story about your life. You will explore transformations of a figure and determine congruence. Within a variety of scenarios, you’ll move your house through a series of transformations, describe the effects, and determine congruence. Graph each transformation described on the coordinate grid under Question 1 in the worksheet. Use a different color for each transformation. Record your answer to each question.
Chapter 1
You are just beginning your life as an adult and have bought a house in a new housing development. Your house is located at A (2,2)
, B (4,2)
, C (4,4)
, D (3,5)
, and E (2,4)
.
Question 1
Plot the points where your house is located, in your favorite color. Name this color here as the color of the original location.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1.
Chapter 2
A flood moves your house exactly 4 blocks to the left and 2 blocks down.
Question 2
Plot and state the points of the new location of your house with a different color. Name the new color you use on your graph here.
Question 3
Describe specifically the formal transformation that occurred when the flood moved your house.
Question 4
Is your new house after this transformation congruent to the original house? Explain your answer.
Chapter 3
You have become an internet sensation after your video received over 5 million views in one week. This made you 1 million dollars. You call a builder and ask them to build you a house twice the size of your current house. The new coordinates of your house are (−4,0), (−4,4), (−2,6), (0,4),
and (0,0).
Question 5
Plot the points of the new house after a scale factor of 2, with the given coordinates. (This is a transformation called dilation.) Use a different color to plot the points. Name the color you use on your graph here.
Question 6
Is your new house after this transformation congruent to the house in Chapter 2? Explain your answer.
Chapter 4
Because you are famous, people want to live near you. You have a new neighbor move in across the street after they build the same exact house as you did in Chapter 3.
Question 7
With a different color, plot and state the points of your neighbor’s house, which is a reflection of your house in Chapter 3 over the y
-axis. Name the color you use on your graph here.
Question 8
Is your new house after this transformation congruent to the house in Chapter 3? Explain your answer.
Chapter 5
A tornado hit the area. It picked up your house and rotated it 180 degrees counterclockwise.
Question 9
Plot and state the points of your new house from Chapter 3 after a counterclockwise rotation of 180 degrees about the origin. Use a different color to plot the points. Name the color you use on your graph here.
Question 10
Is the new location of your house after this transformation congruent to the neighbor’s house in Chapter 4? Explain your answer.
In order to complete this portfolio activity, I will first conduct an internet safe search to find a video explaining the different transformations of a figure on a coordinate plane. I will then watch and listen to the presenter in the video and apply what I have learned to my portfolio.
Once I have done this, I will proceed to answer the questions in the worksheet. Starting with Chapter 1, I will plot the points where my house is located on the coordinate grid using my favorite color. I will then move on to Chapter 2, where a flood moves my house exactly 4 blocks to the left and 2 blocks down. I will plot and state the points of the new location of my house with a different color and describe the specific transformation that occurred. I will also determine if my new house is congruent to the original house after this transformation and provide an explanation for my answer.
Moving on to Chapter 3, I will imagine that my video went viral and I made 1 million dollars. I decide to build a new house twice the size of my current house and provide the new coordinates. I will plot the points of the new house after a scale factor of 2, using a different color, and determine if this transformed house is congruent to the house in Chapter 2. I will again provide an explanation for my answer.
In Chapter 4, I will imagine that a neighbor moves in across the street and builds the same exact house as my house in Chapter 3. I will plot and state the points of my neighbor's house, which will be a reflection of my house over the y-axis, and determine if this transformed house is congruent to the house in Chapter 3. I will provide an explanation for my answer.
Lastly, in Chapter 5, I will assume that a tornado hits the area and rotates my house 180 degrees counterclockwise. I will plot and state the points of my new house after this counterclockwise rotation using a different color. I will then determine if this transformed house is congruent to my neighbor's house in Chapter 4, providing an explanation for my answer.
Once I have completed all the questions, I will save my worksheet with my answers and submit it for a portfolio grade.