Question
Answer the questions:
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 the following points: 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, using your favorite color. Name this color as the "original location color."
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 using a different color. Identify this new color here.
Question 3: Describe 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, earning you 1 million dollars. You call a builder and ask them to construct a house that is twice the size of your current house. The coordinates of your new house are (–4, 0), (–4, 4), (–2, 6), (0, 4), and (0, 0).
Question 5: Plot the points of the new house after applying a scale factor of 2 to the given coordinates. This transformation is called dilation. Use a different color to plot these points and name this color.
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, new residents want to live nearby. A neighbor moves in across the street and builds the same exact house as you did in Chapter 3.
Question 7: Using a different color, plot and state the points of your neighbor’s house, which is a reflection of your house from Chapter 3 over the y-axis. Name the color that you use on your graph.
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, picking up your house and rotating it 180 degrees counterclockwise.
Question 9: Plot and state the points of your house from Chapter 3 after a counterclockwise rotation of 180 degrees about the origin. Use a different color for this plot and name the color you use on your graph.
Question 10: Is the new location of your house after this transformation congruent to your neighbor’s house in Chapter 4? Explain your answer.
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 the following points: 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, using your favorite color. Name this color as the "original location color."
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 using a different color. Identify this new color here.
Question 3: Describe 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, earning you 1 million dollars. You call a builder and ask them to construct a house that is twice the size of your current house. The coordinates of your new house are (–4, 0), (–4, 4), (–2, 6), (0, 4), and (0, 0).
Question 5: Plot the points of the new house after applying a scale factor of 2 to the given coordinates. This transformation is called dilation. Use a different color to plot these points and name this color.
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, new residents want to live nearby. A neighbor moves in across the street and builds the same exact house as you did in Chapter 3.
Question 7: Using a different color, plot and state the points of your neighbor’s house, which is a reflection of your house from Chapter 3 over the y-axis. Name the color that you use on your graph.
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, picking up your house and rotating it 180 degrees counterclockwise.
Question 9: Plot and state the points of your house from Chapter 3 after a counterclockwise rotation of 180 degrees about the origin. Use a different color for this plot and name the color you use on your graph.
Question 10: Is the new location of your house after this transformation congruent to your neighbor’s house in Chapter 4? Explain your answer.
Answers
Answered by
GPT-4o mini
Let's go through the questions step by step.
### Chapter 1
**Question 1:**
Plot the points where your house is located using your favorite color. Let's say my "original location color" is blue. The points are as follows:
- A (2, 2)
- B (4, 2)
- C (4, 4)
- D (3, 5)
- E (2, 4)
### Chapter 2
**Question 2:**
After the flood, your house moves 4 blocks to the left and 2 blocks down:
- A (2 - 4, 2 - 2) = (-2, 0)
- B (4 - 4, 2 - 2) = (0, 0)
- C (4 - 4, 4 - 2) = (0, 2)
- D (3 - 4, 5 - 2) = (-1, 3)
- E (2 - 4, 4 - 2) = (-2, 2)
The new points are:
- A' (-2, 0)
- B' (0, 0)
- C' (0, 2)
- D' (-1, 3)
- E' (-2, 2)
Let's say my "new location color" is green.
**Question 3:**
The formal transformation that occurred is a translation. Specifically, it's a translation of (-4, -2) applied to each point of the original house.
**Question 4:**
Yes, your new house is congruent to the original house. Congruence means that the shapes are the same in size and form, even though they are in different locations. The translation does not alter the size or shape of the house.
### Chapter 3
**Question 5:**
To create a new house using a scale factor of 2 based on the coordinates from your original house (in Chapter 2):
- A' (-2, 0) becomes (-2 * 2, 0 * 2) = (-4, 0)
- B' (0, 0) becomes (0 * 2, 0 * 2) = (0, 0)
- C' (0, 2) becomes (0 * 2, 2 * 2) = (0, 4)
- D' (-1, 3) becomes (-1 * 2, 3 * 2) = (-2, 6)
- E' (-2, 2) becomes (-2 * 2, 2 * 2) = (-4, 4)
So the new coordinates are:
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
Let's say my "dilated house color" is red.
**Question 6:**
No, your new house after this transformation is not congruent to the house in Chapter 2. Dilation changes the size of the figure; thus, while they may have the same shape, the new house is larger and not congruent to the previous one.
### Chapter 4
**Question 7:**
The reflection of the house from Chapter 3 over the y-axis involves taking each x-coordinate and making it negative:
- A'' (–4, 0) becomes (4, 0)
- B'' (0, 0) becomes (0, 0)
- C'' (0, 4) becomes (0, 4)
- D'' (–2, 6) becomes (2, 6)
- E'' (–4, 4) becomes (4, 4)
New neighbor coordinates are:
- A''' (4, 0)
- B''' (0, 0)
- C''' (0, 4)
- D''' (2, 6)
- E''' (4, 4)
Let's say my "neighbor's house color" is orange.
**Question 8:**
Yes, the new house after the reflection is congruent to the house in Chapter 3. This is because reflections preserve distances and angles, thus maintaining the size and shape of the figure.
### Chapter 5
**Question 9:**
After rotating the house from Chapter 3 180 degrees counterclockwise about the origin, we negate both coordinates of each point:
- A'' (–4, 0) becomes (4, 0)
- B'' (0, 0) becomes (0, 0)
- C'' (0, 4) becomes (0, -4)
- D'' (–2, 6) becomes (2, -6)
- E'' (–4, 4) becomes (4, -4)
New points after rotation are:
- A'''' (4, 0)
- B'''' (0, 0)
- C'''' (0, -4)
- D'''' (2, -6)
- E'''' (4, -4)
Let's say my "rotated house color" is purple.
**Question 10:**
Yes, the new location of your house after the transformation is congruent to your neighbor's house in Chapter 4. Both the house after rotation and the reflected house are congruent since transformations such as rotation and reflection preserve the size and shape of the figures involved.
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Feel free to provide any specific colors you'd like to use instead!
### Chapter 1
**Question 1:**
Plot the points where your house is located using your favorite color. Let's say my "original location color" is blue. The points are as follows:
- A (2, 2)
- B (4, 2)
- C (4, 4)
- D (3, 5)
- E (2, 4)
### Chapter 2
**Question 2:**
After the flood, your house moves 4 blocks to the left and 2 blocks down:
- A (2 - 4, 2 - 2) = (-2, 0)
- B (4 - 4, 2 - 2) = (0, 0)
- C (4 - 4, 4 - 2) = (0, 2)
- D (3 - 4, 5 - 2) = (-1, 3)
- E (2 - 4, 4 - 2) = (-2, 2)
The new points are:
- A' (-2, 0)
- B' (0, 0)
- C' (0, 2)
- D' (-1, 3)
- E' (-2, 2)
Let's say my "new location color" is green.
**Question 3:**
The formal transformation that occurred is a translation. Specifically, it's a translation of (-4, -2) applied to each point of the original house.
**Question 4:**
Yes, your new house is congruent to the original house. Congruence means that the shapes are the same in size and form, even though they are in different locations. The translation does not alter the size or shape of the house.
### Chapter 3
**Question 5:**
To create a new house using a scale factor of 2 based on the coordinates from your original house (in Chapter 2):
- A' (-2, 0) becomes (-2 * 2, 0 * 2) = (-4, 0)
- B' (0, 0) becomes (0 * 2, 0 * 2) = (0, 0)
- C' (0, 2) becomes (0 * 2, 2 * 2) = (0, 4)
- D' (-1, 3) becomes (-1 * 2, 3 * 2) = (-2, 6)
- E' (-2, 2) becomes (-2 * 2, 2 * 2) = (-4, 4)
So the new coordinates are:
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
Let's say my "dilated house color" is red.
**Question 6:**
No, your new house after this transformation is not congruent to the house in Chapter 2. Dilation changes the size of the figure; thus, while they may have the same shape, the new house is larger and not congruent to the previous one.
### Chapter 4
**Question 7:**
The reflection of the house from Chapter 3 over the y-axis involves taking each x-coordinate and making it negative:
- A'' (–4, 0) becomes (4, 0)
- B'' (0, 0) becomes (0, 0)
- C'' (0, 4) becomes (0, 4)
- D'' (–2, 6) becomes (2, 6)
- E'' (–4, 4) becomes (4, 4)
New neighbor coordinates are:
- A''' (4, 0)
- B''' (0, 0)
- C''' (0, 4)
- D''' (2, 6)
- E''' (4, 4)
Let's say my "neighbor's house color" is orange.
**Question 8:**
Yes, the new house after the reflection is congruent to the house in Chapter 3. This is because reflections preserve distances and angles, thus maintaining the size and shape of the figure.
### Chapter 5
**Question 9:**
After rotating the house from Chapter 3 180 degrees counterclockwise about the origin, we negate both coordinates of each point:
- A'' (–4, 0) becomes (4, 0)
- B'' (0, 0) becomes (0, 0)
- C'' (0, 4) becomes (0, -4)
- D'' (–2, 6) becomes (2, -6)
- E'' (–4, 4) becomes (4, -4)
New points after rotation are:
- A'''' (4, 0)
- B'''' (0, 0)
- C'''' (0, -4)
- D'''' (2, -6)
- E'''' (4, -4)
Let's say my "rotated house color" is purple.
**Question 10:**
Yes, the new location of your house after the transformation is congruent to your neighbor's house in Chapter 4. Both the house after rotation and the reflected house are congruent since transformations such as rotation and reflection preserve the size and shape of the figures involved.
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Feel free to provide any specific colors you'd like to use instead!