Directions: Use this worksheet to record your answers to the house transformations

Question

in the Transformations and Congruence Portfolio. When you are finished, save this
worksheet with your answers and submit it for a portfolio grade.
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 answers below. Directions: Use this worksheet to record your answers to the house transformations
in the Transformations and Congruence Portfolio. When you are finished, save this
worksheet with your answers and submit it for a portfolio grade.
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 answers below.

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),
E (2,4).

Answer 1

To begin, let's graph the original house on the coordinate grid. We will use the points A, B, C, D, and E to represent the corners of the house.

The original house can be represented by the following coordinates:

A (2,2)
B (4,2)
C (4,4)
D (3,5)
E (2,4)

Let's plot these points on the coordinate grid.


E(2,4)


A(2,2)


D(3,5)


C(4,4)


B(4,2)

Now, let's begin with the transformations.

Transformation 1: Translation

The house is translated 3 units to the right and 2 units up.

New coordinates:

A (5,4)
B (7,4)
C (7,6)
D (6,7)
E (5,6)

Transformation 2: Reflection

The house is reflected over the y-axis.

New coordinates:

A (-5,4)
B (-7,4)
C (-7,6)
D (-6,7)
E (-5,6)

Transformation 3: Rotation

The house is rotated 90 degrees counterclockwise around the origin.

New coordinates:

A (-4,2)
B (-4,4)
C (-6,4)
D (-7,3)
E (-6,2)

Transformation 4: Dilation

The house is dilated with a scale factor of 2.

New coordinates:

A (4,2)
B (8,2)
C (8,8)
D (6,10)
E (4,8)

Transformation 5: Combination of Reflection and Translation

The house is reflected over the line y = x and then translated 2 units to the left and 1 unit down.

New coordinates:

A (-7,5)
B (-9,5)
C (-9,7)
D (-8,8)
E (-7,7)

Now that we have graphed each transformation, we can analyze the effects and determine congruence:

Transformation 1: The house has been shifted to the right and up.
Transformation 2: The house has been flipped over the y-axis.
Transformation 3: The house has been rotated 90 degrees counterclockwise around the origin.
Transformation 4: The house has been enlarged or scaled up.
Transformation 5: The house has been reflected over the line y = x and then shifted to the left and down.

To determine congruence, we compare the side lengths and angles of the original house and the transformed house. If they are equal, then the two houses are congruent.

Answer 2

put in first person instead of saying we

Answer 3

To begin, I will graph the original house on the coordinate grid. I will use the points A, B, C, D, and E to represent the corners of the house.

The original house can be represented by the following coordinates:

A (2,2)
B (4,2)
C (4,4)
D (3,5)
E (2,4)

I will plot these points on the coordinate grid.


E(2,4)


A(2,2)


D(3,5)


C(4,4)


B(4,2)

Now, let's begin with the transformations.

Transformation 1: Translation

I will translate the house 3 units to the right and 2 units up.

New coordinates:

A (5,4)
B (7,4)
C (7,6)
D (6,7)
E (5,6)

Transformation 2: Reflection

I will reflect the house over the y-axis.

New coordinates:

A (-5,4)
B (-7,4)
C (-7,6)
D (-6,7)
E (-5,6)

Transformation 3: Rotation

I will rotate the house 90 degrees counterclockwise around the origin.

New coordinates:

A (-4,2)
B (-4,4)
C (-6,4)
D (-7,3)
E (-6,2)

Transformation 4: Dilation

I will dilate the house with a scale factor of 2.

New coordinates:

A (4,2)
B (8,2)
C (8,8)
D (6,10)
E (4,8)

Transformation 5: Combination of Reflection and Translation

I will reflect the house over the line y = x and then translate it 2 units to the left and 1 unit down.

New coordinates:

A (-7,5)
B (-9,5)
C (-9,7)
D (-8,8)
E (-7,7)

Now that I have graphed each transformation, I can analyze the effects and determine congruence:

Transformation 1: The house has been shifted to the right and up.
Transformation 2: The house has been flipped over the y-axis.
Transformation 3: The house has been rotated 90 degrees counterclockwise around the origin.
Transformation 4: The house has been enlarged or scaled up.
Transformation 5: The house has been reflected over the line y = x and then shifted to the left and down.

To determine congruence, I compare the side lengths and angles of the original house and the transformed house. If they are equal, then the two houses are congruent.