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. blue
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. (x,y) for all 5 points (x,y) (x,y) (x,y) (x,y) (x,y)
Question 3
Describe specifically the formal transformation (write the translation using arrow notation (x +/- ?, y +/-?) that occurred when the flood moved your house.
Question 4 ls 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.
Question 5
Plot the points of the new house after a scale factor of 2 (applied to house in Question 2)with the given coordinates. (This is a transformation called dilation.) Use a different color to plot the points. Name the
Is your new house after this transformation congruent to the house in chapter 2? Or is it an enlargement or reductions? Explain your answer.
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. blue
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. (x,y) for all 5 points (x,y) (x,y) (x,y) (x,y) (x,y)
Question 3
Describe specifically the formal transformation (write the translation using arrow notation (x +/- ?, y +/-?) that occurred when the flood moved your house.
Question 4 ls 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.
Question 5
Plot the points of the new house after a scale factor of 2 (applied to house in Question 2)with the given coordinates. (This is a transformation called dilation.) Use a different color to plot the points. Name the
Is your new house after this transformation congruent to the house in chapter 2? Or is it an enlargement or reductions? Explain your answer.
Answers
GPT-4o mini
### Chapter 1
You are just beginning your life as an adult and have bought a house in a new housing development.
**Original House Points:**
- A (2,2)
- B (4,2)
- C (4,4)
- D (3,5)
- E (2,4)
**Favorite Color:** Blue
### Chapter 2
A flood moves your house exactly 4 blocks to the left and 2 blocks down.
#### Question 2
**New Location of the House:**
- A (2-4, 2-2) = A' (-2, 0)
- B (4-4, 2-2) = B' (0, 0)
- C (4-4, 4-2) = C' (0, 2)
- D (3-4, 5-2) = D' (-1, 3)
- E (2-4, 4-2) = E' (-2, 2)
**New Points:**
- A' (-2, 0)
- B' (0, 0)
- C' (0, 2)
- D' (-1, 3)
- E' (-2, 2)
**New Color:** Red
#### Question 3
**Formal Transformation:**
The translation that occurred when the flood moved your house can be expressed as:
\[ (x, y) \rightarrow (x - 4, y - 2) \]
#### Question 4
**Congruence:**
Yes, your new house after this transformation is congruent to the original house. The transformation involved a translation, which does not change the shape or size of geometric figures. Congruent figures retain the same dimensions and angles.
### 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.
#### Question 5
**Dilation with a Scale Factor of 2:**
To find the new house points after applying a scale factor of 2 to the coordinates of the new location from Question 2, we multiply each coordinate by 2:
- A' (-2, 0) = A'' (-4, 0)
- B' (0, 0) = B'' (0, 0)
- C' (0, 2) = C'' (0, 4)
- D' (-1, 3) = D'' (-2, 6)
- E' (-2, 2) = E'' (-4, 4)
**New House Points after Dilation:**
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
**New Color:** Green
**Congruence Explanation:**
The new house after this transformation is not congruent to the house in Chapter 2. Instead, it is an enlargement. The dilation transformation increased the dimensions of the house twice its original size, which means the angles remain the same, but the shape has changed in scale.
You are just beginning your life as an adult and have bought a house in a new housing development.
**Original House Points:**
- A (2,2)
- B (4,2)
- C (4,4)
- D (3,5)
- E (2,4)
**Favorite Color:** Blue
### Chapter 2
A flood moves your house exactly 4 blocks to the left and 2 blocks down.
#### Question 2
**New Location of the House:**
- A (2-4, 2-2) = A' (-2, 0)
- B (4-4, 2-2) = B' (0, 0)
- C (4-4, 4-2) = C' (0, 2)
- D (3-4, 5-2) = D' (-1, 3)
- E (2-4, 4-2) = E' (-2, 2)
**New Points:**
- A' (-2, 0)
- B' (0, 0)
- C' (0, 2)
- D' (-1, 3)
- E' (-2, 2)
**New Color:** Red
#### Question 3
**Formal Transformation:**
The translation that occurred when the flood moved your house can be expressed as:
\[ (x, y) \rightarrow (x - 4, y - 2) \]
#### Question 4
**Congruence:**
Yes, your new house after this transformation is congruent to the original house. The transformation involved a translation, which does not change the shape or size of geometric figures. Congruent figures retain the same dimensions and angles.
### 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.
#### Question 5
**Dilation with a Scale Factor of 2:**
To find the new house points after applying a scale factor of 2 to the coordinates of the new location from Question 2, we multiply each coordinate by 2:
- A' (-2, 0) = A'' (-4, 0)
- B' (0, 0) = B'' (0, 0)
- C' (0, 2) = C'' (0, 4)
- D' (-1, 3) = D'' (-2, 6)
- E' (-2, 2) = E'' (-4, 4)
**New House Points after Dilation:**
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
**New Color:** Green
**Congruence Explanation:**
The new house after this transformation is not congruent to the house in Chapter 2. Instead, it is an enlargement. The dilation transformation increased the dimensions of the house twice its original size, which means the angles remain the same, but the shape has changed in scale.