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) . Drag and drop the points where your house is located .
Drag and Drop each point to identify your house location.2
B (4,2)
3
C(4,4)
4
E(2,4)
5
D(3,5)
Question 2
QUESTION 2: Choose the correct location of the house after the flood
A flood moves your house exactly 4 blocks to the left and 2 blocks down
What are your new coordinates for the location of the house?
HINT: 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)
finish this for each coordinate on paper, then choose the correct answers below
Responses
New coordinates are A( -2,0), B (4, 2), C(0, 2) , D(-2, 3) E( -2, 2)
New coordinates are A( -2,0), B (4, 2), C(0, 2) , D(-2, 3) E( -2, 2) - no response given
New coordinates are A( -2,0), B (1, 2), C(0, 2) , D(-1, 4) E( -2, 2)
New coordinates are A( -2,0), B (1, 2), C(0, 2) , D(-1, 4) E( -2, 2) - no response given
New coordinates are A( -2,0), B (0, 2), C(0, 2) , D(-1, 3) E( -2, 2)
New coordinates are A( -2,0), B (0, 2), C(0, 2) , D(-1, 3) E( -2, 2) - not selected, this is the correct answer
New coordinates are A( -2,0), B (0, 2), C(2, 2) , D(-1, 3) E( 4, 2)
New coordinates are A( -2,0), B (0, 2), C(2, 2) , D(-1, 3) E( 4, 2) - no response given
Question 3
QUESTION 3
Describe Specifically the formal transformation that occured when the flood moved the house.
HINT: look back at the correct points and question and explain in words what happened.
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Question 4
QUESTION 4:
Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.1Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.2Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.3Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.4Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.5
Correct answers:
1
A( -2,0)
2
B (0, 0)
3
C(0, 2)
4
D(-1, 3)
5
E( -2, 2)
Question 5
QUESTION 5
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.
HINT: multiply 2 by each x and y, example ( 2x, 2y) , The new coordinate for A 1,
The new coordinate for B 2
The new coordinate for C 3
The new coordinate for D 4
The new coordinate for E 5
(4,4)(6,10)(4,8)(8,8)(8,4)
Correct answers:
1
(4,4)
2
(8,4)
3
(8,8)
4
(6,10)
5
(4,8)
Question 6
QUESTION 6
Plot the new coordinates from the above action. Make sure you note the dialation from the first graph.
Dilation is a transformation that changes the size of a shape without altering its basic form , it can enlarge or shrink. Keep this in mind to explain what happened
A(4,4)
2
B(8,4)
3
C((8,8)
4
D(6,10)
5
E(4,8)
Question 7
QUESTION 7
Explain the dialation using the coordinates and language to describe what happened to your house from the first location in quesiton 1, to the final location in Question 6.
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Question 8
QUESTION, QUESTION 8
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 #7. 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))
A
1
B
2
C
3
D
4
E
5
(-6,10)(-4,4)(-8,4)(-8,8)(-4,8)
Correct answers:
1
(-4,4)
2
(-8,4)
3
(-8,8)
4
(-6,10)
5
(-4,8)
Question 9
QUESTION 9
Explain the new transformation over the y axis, then explain if this house is congruent to your neighbors house.
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Question 10
QUESTION 10
Match the correct definition to the word used in our lessons
HINT : Check out the Vocabulary in the Lesson intro pages.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Line of Symmetry
1
Reflection
2
Rotation
3
Rotation Symmetry
4
Transformation
5
Translation
6
Isometry
7
Dilation
8
Pre Image
9
Image
10
Shrink
11
Line of Reflection
12
degree of rotation
13
Clockwise
14
Scale Factor
15
Translation
16
Englargement/Expansion
17
a type of transformation that uses a line that acts as a mirror with an image reflected in the linea figure in the plane has this if the figure can be mapped onto itself by a rotation of 180 degrees or lessa type of composite or combination transformation of a reflection over a line followed by a translation or vice versathe operation that maps, or moves, a preimage onto an image.a line that a figure in the plane has if the figure can be mapped onto itself by a reflection in the linealso known as the angle of rotation; the measure of degrees that a figure is rotated about a fixed pointa type of transformation that maps every 2 points P and Q in the plane to points P' and Q' so that PP'=QQ', PP' is parallel to QQ', or PP' and QQ' are collineara transformation that preserves lengths; aka rigid transformationa type of transformation in which a figure is turned about a fixed pointmotion that proceeds in the same direction as the hands of a clock, from top right, down, then left, back to the top; in math it is in the negative degree directiona dilation transformation in which the scale factor is more than 1 which causes the image to be larger, stretched, or expanded, yet is similar (same shape, different size) to the original preimagethe new figure that results from the transformation of a figure in a planea dilation with a scale factor less than 1 which reduces the size of the original figurea line that acts as a mirror and reflects an image for a transformationthe original figure in the transformation of a figure in a planea type of transformation, with center C and scale factor k, that maps every point P in the plane to a point P'the k or the multiplier of a dilation
Drag and Drop each point to identify your house location.2
B (4,2)
3
C(4,4)
4
E(2,4)
5
D(3,5)
Question 2
QUESTION 2: Choose the correct location of the house after the flood
A flood moves your house exactly 4 blocks to the left and 2 blocks down
What are your new coordinates for the location of the house?
HINT: 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)
finish this for each coordinate on paper, then choose the correct answers below
Responses
New coordinates are A( -2,0), B (4, 2), C(0, 2) , D(-2, 3) E( -2, 2)
New coordinates are A( -2,0), B (4, 2), C(0, 2) , D(-2, 3) E( -2, 2) - no response given
New coordinates are A( -2,0), B (1, 2), C(0, 2) , D(-1, 4) E( -2, 2)
New coordinates are A( -2,0), B (1, 2), C(0, 2) , D(-1, 4) E( -2, 2) - no response given
New coordinates are A( -2,0), B (0, 2), C(0, 2) , D(-1, 3) E( -2, 2)
New coordinates are A( -2,0), B (0, 2), C(0, 2) , D(-1, 3) E( -2, 2) - not selected, this is the correct answer
New coordinates are A( -2,0), B (0, 2), C(2, 2) , D(-1, 3) E( 4, 2)
New coordinates are A( -2,0), B (0, 2), C(2, 2) , D(-1, 3) E( 4, 2) - no response given
Question 3
QUESTION 3
Describe Specifically the formal transformation that occured when the flood moved the house.
HINT: look back at the correct points and question and explain in words what happened.
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Question 4
QUESTION 4:
Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.1Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.2Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.3Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.4Select responses from the drop down fields to answer the question. Navigate to the desired drop down and select your response.5
Correct answers:
1
A( -2,0)
2
B (0, 0)
3
C(0, 2)
4
D(-1, 3)
5
E( -2, 2)
Question 5
QUESTION 5
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.
HINT: multiply 2 by each x and y, example ( 2x, 2y) , The new coordinate for A 1,
The new coordinate for B 2
The new coordinate for C 3
The new coordinate for D 4
The new coordinate for E 5
(4,4)(6,10)(4,8)(8,8)(8,4)
Correct answers:
1
(4,4)
2
(8,4)
3
(8,8)
4
(6,10)
5
(4,8)
Question 6
QUESTION 6
Plot the new coordinates from the above action. Make sure you note the dialation from the first graph.
Dilation is a transformation that changes the size of a shape without altering its basic form , it can enlarge or shrink. Keep this in mind to explain what happened
A(4,4)
2
B(8,4)
3
C((8,8)
4
D(6,10)
5
E(4,8)
Question 7
QUESTION 7
Explain the dialation using the coordinates and language to describe what happened to your house from the first location in quesiton 1, to the final location in Question 6.
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Question 8
QUESTION, QUESTION 8
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 #7. 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))
A
1
B
2
C
3
D
4
E
5
(-6,10)(-4,4)(-8,4)(-8,8)(-4,8)
Correct answers:
1
(-4,4)
2
(-8,4)
3
(-8,8)
4
(-6,10)
5
(-4,8)
Question 9
QUESTION 9
Explain the new transformation over the y axis, then explain if this house is congruent to your neighbors house.
Audio Player
No audio to playback
-:-- / -:--
Question 10
QUESTION 10
Match the correct definition to the word used in our lessons
HINT : Check out the Vocabulary in the Lesson intro pages.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Line of Symmetry
1
Reflection
2
Rotation
3
Rotation Symmetry
4
Transformation
5
Translation
6
Isometry
7
Dilation
8
Pre Image
9
Image
10
Shrink
11
Line of Reflection
12
degree of rotation
13
Clockwise
14
Scale Factor
15
Translation
16
Englargement/Expansion
17
a type of transformation that uses a line that acts as a mirror with an image reflected in the linea figure in the plane has this if the figure can be mapped onto itself by a rotation of 180 degrees or lessa type of composite or combination transformation of a reflection over a line followed by a translation or vice versathe operation that maps, or moves, a preimage onto an image.a line that a figure in the plane has if the figure can be mapped onto itself by a reflection in the linealso known as the angle of rotation; the measure of degrees that a figure is rotated about a fixed pointa type of transformation that maps every 2 points P and Q in the plane to points P' and Q' so that PP'=QQ', PP' is parallel to QQ', or PP' and QQ' are collineara transformation that preserves lengths; aka rigid transformationa type of transformation in which a figure is turned about a fixed pointmotion that proceeds in the same direction as the hands of a clock, from top right, down, then left, back to the top; in math it is in the negative degree directiona dilation transformation in which the scale factor is more than 1 which causes the image to be larger, stretched, or expanded, yet is similar (same shape, different size) to the original preimagethe new figure that results from the transformation of a figure in a planea dilation with a scale factor less than 1 which reduces the size of the original figurea line that acts as a mirror and reflects an image for a transformationthe original figure in the transformation of a figure in a planea type of transformation, with center C and scale factor k, that maps every point P in the plane to a point P'the k or the multiplier of a dilation
Answers
Answered by
GPT-4o mini
Let's go through the questions step by step with the given information:
**Question 1: Identify the House Location**
You have points A(2,2), B(4,2), C(4,4), D(3,5), and E(2,4).
Identifying the location:
- A: (2, 2)
- B: (4, 2)
- C: (4, 4)
- D: (3, 5)
- E: (2, 4)
This step doesn't require an action as it just establishes your house locations.
---
**Question 2: New coordinates after the flood**
The flood moves your house exactly 4 blocks to the left and 2 blocks down.
Apply the transformation (x - 4, y - 2) to each coordinate:
1. **A(2,2)**:
- x: 2 - 4 = -2
- y: 2 - 2 = 0
- New coordinates: A(-2, 0)
2. **B(4,2)**:
- x: 4 - 4 = 0
- y: 2 - 2 = 0
- New coordinates: B(0, 0)
3. **C(4,4)**:
- x: 4 - 4 = 0
- y: 4 - 2 = 2
- New coordinates: C(0, 2)
4. **D(3,5)**:
- x: 3 - 4 = -1
- y: 5 - 2 = 3
- New coordinates: D(-1, 3)
5. **E(2,4)**:
- x: 2 - 4 = -2
- y: 4 - 2 = 2
- New coordinates: E(-2, 2)
Correct responses from the choices:
- New coordinates are:
- A: (-2,0)
- B: (0,0)
- C: (0,2)
- D: (-1,3)
- E: (-2,2)
So the answer correctly matches to **New coordinates are A(-2, 0), B(0, 0), C(0, 2), D(-1, 3), E(-2, 2)**.
---
**Question 3: Describe the Transformation**
The formal transformation that occurred during the flood was a translation of the house coordinates 4 units to the left and 2 units down. This means each x-coordinate was decreased by 4, and each y-coordinate was decreased by 2. As a result, the house locations changed to new coordinates that are effectively repositioned in a lower left quadrant in relation to their original positions.
---
**Question 4: Select Responses**
1. A(-2,0)
2. B(0,0)
3. C(0,2)
4. D(-1,3)
5. E(-2,2)
---
**Question 5: New coordinates for double the original size**
Multiply each coordinate by 2:
1. **A(2,2)**: (2*2, 2*2) = (4,4)
2. **B(4,2)**: (4*2, 2*2) = (8,4)
3. **C(4,4)**: (4*2, 4*2) = (8,8)
4. **D(3,5)**: (3*2, 5*2) = (6,10)
5. **E(2,4)**: (2*2, 4*2) = (4,8)
Correct responses:
1. (4,4)
2. (8,4)
3. (8,8)
4. (6,10)
5. (4,8)
---
**Question 6: Plot the New Coordinates**
Plotting these new coordinates indicates a dilation transformation. Dilation, in this context, means the house has been enlarged to twice its original dimensions while preserving the same shape.
The points are:
- A(4, 4)
- B(8, 4)
- C(8, 8)
- D(6, 10)
- E(4, 8)
---
**Question 7: Dilation Explanation**
The dilation from the original points A(2,2) through E(2,4) to the final points A(4,4) through E(4,8) shows that each coordinate was scaled up by a factor of 2. While the house size increased, the orientations and relative distances remained unchanged, indicating a similarity in shape despite the change in size.
---
**Question 8: Neighbor's House new Coordinates**
To reflect the coordinates across the y-axis, change the sign of the x-coordinates:
- A(4, 4) becomes (-4, 4)
- B(8, 4) becomes (-8, 4)
- C(8, 8) becomes (-8, 8)
- D(6, 10) becomes (-6, 10)
- E(4, 8) becomes (-4, 8)
Correct responses:
1. (-4, 4)
2. (-8, 4)
3. (-8, 8)
4. (-6, 10)
5. (-4, 8)
---
**Question 9: Explain the New Transformation**
The new transformation over the y-axis involved reflecting each house coordinate across the vertical axis. This process effectively mirrored the position of the house at the new coordinates while maintaining the same shape and size of the house. Since both houses are congruent after reflection, the structure and interior options remain identical, just positioned symmetrically relative to the y-axis.
---
**Question 10: Match Definitions**
1. Line of Symmetry - a line that acts as a mirror and reflects an image for a transformation.
2. Reflection - a type of composite or combination transformation of a reflection over a line followed by a translation or vice versa.
3. Rotation - a type of transformation in which a figure is turned about a fixed point.
4. Rotation Symmetry - a figure in the plane has this if the figure can be mapped onto itself by a rotation of 180 degrees or less.
5. Transformation - the operation that maps, or moves, a preimage onto an image.
6. Translation - a type of transformation that maps every 2 points P and Q in the plane to points P' and Q'.
7. Isometry - a transformation that preserves lengths; aka rigid transformation.
8. Dilation - a type of transformation, with center C and scale factor k, that maps every point P in the plane to a point P'.
9. Pre Image - the original figure in the transformation of a figure in a plane.
10. Image - the new figure that results from the transformation of a figure in a plane.
11. Shrink - a dilation with a scale factor less than 1 which reduces the size of the original figure.
12. Line of Reflection - a line that a figure in the plane has if the figure can be mapped onto itself by a reflection in the line.
13. Degree of rotation - also known as the angle of rotation; the measure of degrees that a figure is rotated about a fixed point.
14. Clockwise - motion that proceeds in the same direction as the hands of a clock, from top right, down, then left, back to the top.
15. Scale Factor - the k or the multiplier of a dilation.
16. Enlargement/Expansion - a dilation transformation in which the scale factor is more than 1 which causes the image to be larger, stretched, or expanded, yet is similar (same shape, different size) to the original preimage.
This concludes the provided transformation-related questions. If you have any other questions or need further assistance, feel free to ask!
**Question 1: Identify the House Location**
You have points A(2,2), B(4,2), C(4,4), D(3,5), and E(2,4).
Identifying the location:
- A: (2, 2)
- B: (4, 2)
- C: (4, 4)
- D: (3, 5)
- E: (2, 4)
This step doesn't require an action as it just establishes your house locations.
---
**Question 2: New coordinates after the flood**
The flood moves your house exactly 4 blocks to the left and 2 blocks down.
Apply the transformation (x - 4, y - 2) to each coordinate:
1. **A(2,2)**:
- x: 2 - 4 = -2
- y: 2 - 2 = 0
- New coordinates: A(-2, 0)
2. **B(4,2)**:
- x: 4 - 4 = 0
- y: 2 - 2 = 0
- New coordinates: B(0, 0)
3. **C(4,4)**:
- x: 4 - 4 = 0
- y: 4 - 2 = 2
- New coordinates: C(0, 2)
4. **D(3,5)**:
- x: 3 - 4 = -1
- y: 5 - 2 = 3
- New coordinates: D(-1, 3)
5. **E(2,4)**:
- x: 2 - 4 = -2
- y: 4 - 2 = 2
- New coordinates: E(-2, 2)
Correct responses from the choices:
- New coordinates are:
- A: (-2,0)
- B: (0,0)
- C: (0,2)
- D: (-1,3)
- E: (-2,2)
So the answer correctly matches to **New coordinates are A(-2, 0), B(0, 0), C(0, 2), D(-1, 3), E(-2, 2)**.
---
**Question 3: Describe the Transformation**
The formal transformation that occurred during the flood was a translation of the house coordinates 4 units to the left and 2 units down. This means each x-coordinate was decreased by 4, and each y-coordinate was decreased by 2. As a result, the house locations changed to new coordinates that are effectively repositioned in a lower left quadrant in relation to their original positions.
---
**Question 4: Select Responses**
1. A(-2,0)
2. B(0,0)
3. C(0,2)
4. D(-1,3)
5. E(-2,2)
---
**Question 5: New coordinates for double the original size**
Multiply each coordinate by 2:
1. **A(2,2)**: (2*2, 2*2) = (4,4)
2. **B(4,2)**: (4*2, 2*2) = (8,4)
3. **C(4,4)**: (4*2, 4*2) = (8,8)
4. **D(3,5)**: (3*2, 5*2) = (6,10)
5. **E(2,4)**: (2*2, 4*2) = (4,8)
Correct responses:
1. (4,4)
2. (8,4)
3. (8,8)
4. (6,10)
5. (4,8)
---
**Question 6: Plot the New Coordinates**
Plotting these new coordinates indicates a dilation transformation. Dilation, in this context, means the house has been enlarged to twice its original dimensions while preserving the same shape.
The points are:
- A(4, 4)
- B(8, 4)
- C(8, 8)
- D(6, 10)
- E(4, 8)
---
**Question 7: Dilation Explanation**
The dilation from the original points A(2,2) through E(2,4) to the final points A(4,4) through E(4,8) shows that each coordinate was scaled up by a factor of 2. While the house size increased, the orientations and relative distances remained unchanged, indicating a similarity in shape despite the change in size.
---
**Question 8: Neighbor's House new Coordinates**
To reflect the coordinates across the y-axis, change the sign of the x-coordinates:
- A(4, 4) becomes (-4, 4)
- B(8, 4) becomes (-8, 4)
- C(8, 8) becomes (-8, 8)
- D(6, 10) becomes (-6, 10)
- E(4, 8) becomes (-4, 8)
Correct responses:
1. (-4, 4)
2. (-8, 4)
3. (-8, 8)
4. (-6, 10)
5. (-4, 8)
---
**Question 9: Explain the New Transformation**
The new transformation over the y-axis involved reflecting each house coordinate across the vertical axis. This process effectively mirrored the position of the house at the new coordinates while maintaining the same shape and size of the house. Since both houses are congruent after reflection, the structure and interior options remain identical, just positioned symmetrically relative to the y-axis.
---
**Question 10: Match Definitions**
1. Line of Symmetry - a line that acts as a mirror and reflects an image for a transformation.
2. Reflection - a type of composite or combination transformation of a reflection over a line followed by a translation or vice versa.
3. Rotation - a type of transformation in which a figure is turned about a fixed point.
4. Rotation Symmetry - a figure in the plane has this if the figure can be mapped onto itself by a rotation of 180 degrees or less.
5. Transformation - the operation that maps, or moves, a preimage onto an image.
6. Translation - a type of transformation that maps every 2 points P and Q in the plane to points P' and Q'.
7. Isometry - a transformation that preserves lengths; aka rigid transformation.
8. Dilation - a type of transformation, with center C and scale factor k, that maps every point P in the plane to a point P'.
9. Pre Image - the original figure in the transformation of a figure in a plane.
10. Image - the new figure that results from the transformation of a figure in a plane.
11. Shrink - a dilation with a scale factor less than 1 which reduces the size of the original figure.
12. Line of Reflection - a line that a figure in the plane has if the figure can be mapped onto itself by a reflection in the line.
13. Degree of rotation - also known as the angle of rotation; the measure of degrees that a figure is rotated about a fixed point.
14. Clockwise - motion that proceeds in the same direction as the hands of a clock, from top right, down, then left, back to the top.
15. Scale Factor - the k or the multiplier of a dilation.
16. Enlargement/Expansion - a dilation transformation in which the scale factor is more than 1 which causes the image to be larger, stretched, or expanded, yet is similar (same shape, different size) to the original preimage.
This concludes the provided transformation-related questions. If you have any other questions or need further assistance, feel free to ask!