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
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
Answers
GPT-4o mini
### Chapter 1:
You are 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)
- E (2,4)
**Question 1:**
The points where your house is located will be plotted in blue.
### Chapter 2:
A flood moves your house exactly 4 blocks to the left and 2 blocks down.
**Question 2:**
To find the new location of your house after the flood, we will subtract 4 from the x-coordinates and 2 from the y-coordinates of each point:
- A (2,2) → A' (2 - 4, 2 - 2) = A' (-2, 0)
- B (4,2) → B' (4 - 4, 2 - 2) = B' (0, 0)
- C (4,4) → C' (4 - 4, 4 - 2) = C' (0, 2)
- D (3,5) → D' (3 - 4, 5 - 2) = D' (-1, 3)
- E (2,4) → E' (2 - 4, 4 - 2) = E' (-2, 2)
The new points where your house is located are:
- A' (-2,0)
- B' (0,0)
- C' (0,2)
- D' (-1,3)
- E' (-2,2)
The new color used to plot these points will be green.
**Question 3:**
The formal transformation can be described as:
\[
(x, y) \rightarrow (x - 4, y - 2)
\]
This means the translation is a movement of 4 units to the left and 2 units down.
**Question 4:**
Yes, your new house after this transformation is congruent to the original house. Congruence in geometry means that the two shapes have the same size and shape, even though they may be located in different positions. The flood moved your house without changing the distance between the points or the angles, meaning the sizes are identical.
### Chapter 3:
You have become an internet sensation after your video received over 5 million views in one week, making you 1 million dollars. You ask a builder to build you a house twice the size of your current house.
**Question 5:**
To apply a scale factor of 2 to the new house points (A', B', C', D', E'), we multiply each coordinate by 2:
- A' (-2,0) → A'' (-2 * 2, 0 * 2) = A'' (-4, 0)
- B' (0,0) → B'' (0 * 2, 0 * 2) = B'' (0, 0)
- C' (0,2) → C'' (0 * 2, 2 * 2) = C'' (0, 4)
- D' (-1,3) → D'' (-1 * 2, 3 * 2) = D'' (-2, 6)
- E' (-2,2) → E'' (-2 * 2, 2 * 2) = E'' (-4, 4)
The points of the new house after the dilation (twice the size) are:
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
This transformation can be plotted in orange (for example).
You are 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)
- E (2,4)
**Question 1:**
The points where your house is located will be plotted in blue.
### Chapter 2:
A flood moves your house exactly 4 blocks to the left and 2 blocks down.
**Question 2:**
To find the new location of your house after the flood, we will subtract 4 from the x-coordinates and 2 from the y-coordinates of each point:
- A (2,2) → A' (2 - 4, 2 - 2) = A' (-2, 0)
- B (4,2) → B' (4 - 4, 2 - 2) = B' (0, 0)
- C (4,4) → C' (4 - 4, 4 - 2) = C' (0, 2)
- D (3,5) → D' (3 - 4, 5 - 2) = D' (-1, 3)
- E (2,4) → E' (2 - 4, 4 - 2) = E' (-2, 2)
The new points where your house is located are:
- A' (-2,0)
- B' (0,0)
- C' (0,2)
- D' (-1,3)
- E' (-2,2)
The new color used to plot these points will be green.
**Question 3:**
The formal transformation can be described as:
\[
(x, y) \rightarrow (x - 4, y - 2)
\]
This means the translation is a movement of 4 units to the left and 2 units down.
**Question 4:**
Yes, your new house after this transformation is congruent to the original house. Congruence in geometry means that the two shapes have the same size and shape, even though they may be located in different positions. The flood moved your house without changing the distance between the points or the angles, meaning the sizes are identical.
### Chapter 3:
You have become an internet sensation after your video received over 5 million views in one week, making you 1 million dollars. You ask a builder to build you a house twice the size of your current house.
**Question 5:**
To apply a scale factor of 2 to the new house points (A', B', C', D', E'), we multiply each coordinate by 2:
- A' (-2,0) → A'' (-2 * 2, 0 * 2) = A'' (-4, 0)
- B' (0,0) → B'' (0 * 2, 0 * 2) = B'' (0, 0)
- C' (0,2) → C'' (0 * 2, 2 * 2) = C'' (0, 4)
- D' (-1,3) → D'' (-1 * 2, 3 * 2) = D'' (-2, 6)
- E' (-2,2) → E'' (-2 * 2, 2 * 2) = E'' (-4, 4)
The points of the new house after the dilation (twice the size) are:
- A'' (-4, 0)
- B'' (0, 0)
- C'' (0, 4)
- D'' (-2, 6)
- E'' (-4, 4)
This transformation can be plotted in orange (for example).