Question
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).
Choose the correct location of the house after the flood
A flood moves your house exactly 4 blocks to the eft and 2 blocks down
What are your new coordinates for the location of the house?
(Left and right is X, up and down is y)
Each value must be worked out example below:
(x -4, y -2)
A, (2,2) would be A, (2 -4, 2-2) the NEW coordinates are ( -2, 0)
the answer for this question was C. New coordinates are A( -2, 0), B.(0,0), C(0,2), D(-1, 3), E(-2,2)
Describe Specifically the formal transformation that occurred when the flood moved the house.
HINT: Look back at the correct points and questions and explain in words what happened.
"
You have gone viral after your video received over 5 million views in one week. This made you 1 million dollars. You call the builder and ask them to build you a house twice the size of your current house, the new coordinates are two times the original house, using the original coordinates what are the new coordinates for each house.
The new coordinate for A
The new coordinate for B
The new coordinate for C
The new coordinate for D
The new coordinate for E
Answer choices: (4,4) (6,10) (4,8) (8,8) (8,4)
The original coordinates were A(-2,0), B(0,0), C(0,2), D(-1, 3) E (-2,2)
Explain the dilatation using the coordinates and language to describe what happened to your house from the first location in question 1, to the final location in question 6.
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 the previous question. What are the new coordinates?
Original coordinates are on the left, match with new coordinates.
HINT: See rule for reflection across y axis below
Example the coordinate (2, 4) becomes (-2, 4))
Coordinate Transformations
Translation
Reflection across the x-axis | (x, y) -> (x+a, y+b)
reflection across the y-axis | (x,y) -> (x, -y)
reflection across the line y=x| (x,y) -> (y, x)
Rotation 90° about the origin| (x,y) -> (-y,x)
rotation 180° about the origin| (x,y) -> (-x, -y)
Rotation 270° about the origin| (x,y) -> (y, -x)
Dilation with respect to the origin and scale factor of k|(x,y) -> (kx,ky)
[ A ] (-6, 10)
[ B ] (-4, 4)
[ C ] (-8, 4)
[ D ] (-8, 8)
[ E ] (-4, 8)
the question above has been answered, Explain the new transformation over the y-axis, then explain if this house is congruent to your neighbors house.(give your explanation in under 3 sentences)
Choose the correct location of the house after the flood
A flood moves your house exactly 4 blocks to the eft and 2 blocks down
What are your new coordinates for the location of the house?
(Left and right is X, up and down is y)
Each value must be worked out example below:
(x -4, y -2)
A, (2,2) would be A, (2 -4, 2-2) the NEW coordinates are ( -2, 0)
the answer for this question was C. New coordinates are A( -2, 0), B.(0,0), C(0,2), D(-1, 3), E(-2,2)
Describe Specifically the formal transformation that occurred when the flood moved the house.
HINT: Look back at the correct points and questions and explain in words what happened.
"
You have gone viral after your video received over 5 million views in one week. This made you 1 million dollars. You call the builder and ask them to build you a house twice the size of your current house, the new coordinates are two times the original house, using the original coordinates what are the new coordinates for each house.
The new coordinate for A
The new coordinate for B
The new coordinate for C
The new coordinate for D
The new coordinate for E
Answer choices: (4,4) (6,10) (4,8) (8,8) (8,4)
The original coordinates were A(-2,0), B(0,0), C(0,2), D(-1, 3) E (-2,2)
Explain the dilatation using the coordinates and language to describe what happened to your house from the first location in question 1, to the final location in question 6.
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 the previous question. What are the new coordinates?
Original coordinates are on the left, match with new coordinates.
HINT: See rule for reflection across y axis below
Example the coordinate (2, 4) becomes (-2, 4))
Coordinate Transformations
Translation
Reflection across the x-axis | (x, y) -> (x+a, y+b)
reflection across the y-axis | (x,y) -> (x, -y)
reflection across the line y=x| (x,y) -> (y, x)
Rotation 90° about the origin| (x,y) -> (-y,x)
rotation 180° about the origin| (x,y) -> (-x, -y)
Rotation 270° about the origin| (x,y) -> (y, -x)
Dilation with respect to the origin and scale factor of k|(x,y) -> (kx,ky)
[ A ] (-6, 10)
[ B ] (-4, 4)
[ C ] (-8, 4)
[ D ] (-8, 8)
[ E ] (-4, 8)
the question above has been answered, Explain the new transformation over the y-axis, then explain if this house is congruent to your neighbors house.(give your explanation in under 3 sentences)
Answers
GPT-4o mini
### Transformation After the Flood
1. **New Coordinates Calculation**
- The original coordinates are as follows:
- A(2,2): After flood → A(2 - 4, 2 - 2) → A(-2, 0)
- B(4,2): After flood → B(4 - 4, 2 - 2) → B(0, 0)
- C(4,4): After flood → C(4 - 4, 4 - 2) → C(0, 2)
- D(3,5): After flood → D(3 - 4, 5 - 2) → D(-1, 3)
- E(2,4): After flood → E(2 - 4, 4 - 2) → E(-2, 2)
Therefore, the new coordinates are:
- A(-2, 0)
- B(0, 0)
- C(0, 2)
- D(-1, 3)
- E(-2, 2)
2. **Description of the Transformation**
The transformation that occurred when the flood moved the house was a **translation**. Specifically, the house was moved 4 blocks to the left (subtracting from the x-coordinate) and 2 blocks down (subtracting from the y-coordinate). This resulted in a shift of each point by the vector (-4, -2).
### Dilation of the Coordinates
3. **New Coordinates After Dilation:**
To find the new coordinates after dilating the house by a scale factor of 2, 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)
Assuming the correct multiplication in the original bit, we have:
- A(4, 4)
- B(0, 0)
- C(0, 4)
- D(-2, 6)
- E(-4, 4)
4. **Final Coordinates after Dilation with Correct Matches**
Based on your answer choices, let's represent them accurately:
- A(4, 4) - Matches with B'(0, 0)
- B(0, 0) - Matches with B'(0, 0)
- C(0, 2) - Matches with C'(0, 4)
- D(-1, 3) - Matches with D'(-2, 6)
- E(-2, 2) - Matches with E'(-4, 4)
### Reflection Across the Y-axis
5. **New Coordinates After Reflection**
Reflecting each house's original coordinates across the y-axis:
- A(4, 4) → A(-4, 4)
- B(0, 0) → B(0, 0)
- C(0, 4) → C(0, 4)
- D(-2, 6) → D(2, 6)
- E(-4, 4) → E(4, 4)
6. **Explanation of the Transformation and Congruence**
The reflection across the y-axis involved changing the sign of the x-coordinate of each point, effectively mirroring the house’s coordinates to the opposite side of the y-axis. Overall, the house and the neighboring house remain congruent since they share the same dimensions and shape post-transformation. Congruence is maintained, as reflection preserves distances and angles.
1. **New Coordinates Calculation**
- The original coordinates are as follows:
- A(2,2): After flood → A(2 - 4, 2 - 2) → A(-2, 0)
- B(4,2): After flood → B(4 - 4, 2 - 2) → B(0, 0)
- C(4,4): After flood → C(4 - 4, 4 - 2) → C(0, 2)
- D(3,5): After flood → D(3 - 4, 5 - 2) → D(-1, 3)
- E(2,4): After flood → E(2 - 4, 4 - 2) → E(-2, 2)
Therefore, the new coordinates are:
- A(-2, 0)
- B(0, 0)
- C(0, 2)
- D(-1, 3)
- E(-2, 2)
2. **Description of the Transformation**
The transformation that occurred when the flood moved the house was a **translation**. Specifically, the house was moved 4 blocks to the left (subtracting from the x-coordinate) and 2 blocks down (subtracting from the y-coordinate). This resulted in a shift of each point by the vector (-4, -2).
### Dilation of the Coordinates
3. **New Coordinates After Dilation:**
To find the new coordinates after dilating the house by a scale factor of 2, 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)
Assuming the correct multiplication in the original bit, we have:
- A(4, 4)
- B(0, 0)
- C(0, 4)
- D(-2, 6)
- E(-4, 4)
4. **Final Coordinates after Dilation with Correct Matches**
Based on your answer choices, let's represent them accurately:
- A(4, 4) - Matches with B'(0, 0)
- B(0, 0) - Matches with B'(0, 0)
- C(0, 2) - Matches with C'(0, 4)
- D(-1, 3) - Matches with D'(-2, 6)
- E(-2, 2) - Matches with E'(-4, 4)
### Reflection Across the Y-axis
5. **New Coordinates After Reflection**
Reflecting each house's original coordinates across the y-axis:
- A(4, 4) → A(-4, 4)
- B(0, 0) → B(0, 0)
- C(0, 4) → C(0, 4)
- D(-2, 6) → D(2, 6)
- E(-4, 4) → E(4, 4)
6. **Explanation of the Transformation and Congruence**
The reflection across the y-axis involved changing the sign of the x-coordinate of each point, effectively mirroring the house’s coordinates to the opposite side of the y-axis. Overall, the house and the neighboring house remain congruent since they share the same dimensions and shape post-transformation. Congruence is maintained, as reflection preserves distances and angles.