Question
Use the image to answer the question.
Two quadrilaterals upper A upper B upper C upper D and upper E upper F upper G upper H are marked in the second and fourth quadrants of a coordinate plane respectively.
What reflections or sequence of reflections transforms figure ABCD into figure EFGH?
(1 point)
Responses which is the true correct answer a b c or d and tell me by solving it why it is that one
Reflect ABCD first over the line x=0
, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line x is equal to 0, then over the line y is equal to x .
Reflect ABCD first over the line y=0, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line y is equal to 0 , then over the line y is equal to x .
Reflect ABCD first over the line x=0, then over the line y=0.
Reflect cap A cap b cap c cap d first over the line x is equal to 0 , then over the line y is equal to 0 .
Reflect ABCD over the line y=x
Reflect cap A cap b cap c cap d over the line y is equal to x
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Two quadrilaterals upper A upper B upper C upper D and upper E upper F upper G upper H are marked in the second and fourth quadrants of a coordinate plane respectively.
What reflections or sequence of reflections transforms figure ABCD into figure EFGH?
(1 point)
Responses which is the true correct answer a b c or d and tell me by solving it why it is that one
Reflect ABCD first over the line x=0
, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line x is equal to 0, then over the line y is equal to x .
Reflect ABCD first over the line y=0, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line y is equal to 0 , then over the line y is equal to x .
Reflect ABCD first over the line x=0, then over the line y=0.
Reflect cap A cap b cap c cap d first over the line x is equal to 0 , then over the line y is equal to 0 .
Reflect ABCD over the line y=x
Reflect cap A cap b cap c cap d over the line y is equal to x
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which reflections transform quadrilateral ABCD into quadrilateral EFGH, we need to look at the properties of reflections in a coordinate plane.
Assume:
- Quadrilateral ABCD is located in the second quadrant (where x < 0 and y > 0).
- Quadrilateral EFGH is located in the fourth quadrant (where x > 0 and y < 0).
To go from the second quadrant to the fourth quadrant, the following transformations should occur:
1. **Reflect over the line y=0** (the x-axis): This reflection will take points in the second quadrant to the third quadrant. For example, a point (x, y) will be reflected to (x, -y). So a point in the second quadrant will move to the third quadrant.
2. **Reflect over the line x=0** (the y-axis): This reflection will take points from the third quadrant to the fourth quadrant. For example, a point (x, y) will be reflected to (-x, y), flipping the x-coordinate to negative.
3. **Reflect over the line y=x**: This transformation will swap the x and y coordinates of the shape, but in our case, the quadrilateral is already in place after the first two transformations.
Given these necessary reflections, we can see:
- The transformation sequence that reflects over the line y = 0 first would move ABCD to the third quadrant.
- The subsequent reflection over the line x = 0 would then move it to the fourth quadrant.
Now let's compare the given options:
**Option B**
> Reflect ABCD first over the line y=0, then over the line y=x.
In this option, the first reflection correctly takes ABCD to the third quadrant (which is not what we want) but does not help to get to EFGH.
**Option A**
> Reflect ABCD first over the line x=0, then over the line y=x.
This will not work because the first reflection takes the shape to the left instead of down.
**Option C**
> Reflect ABCD first over the line x=0, then over the line y=0.
This option does not correctly move the shape to the desired position either.
**Option D**
> Reflect ABCD over the line y=x.
This single reflection won't be sufficient to achieve the transformation needed.
Based on the analysis:
The **correct transformations** are achieved by reflecting ABCD **first over y=0 (the x-axis)**, then **over x=0 (the y-axis)**. This will correctly position ABCD transformed into EFGH.
Thus, the **correct response is**:
**Reflect ABCD first over the line y=0, then over the line y=x.**
Assume:
- Quadrilateral ABCD is located in the second quadrant (where x < 0 and y > 0).
- Quadrilateral EFGH is located in the fourth quadrant (where x > 0 and y < 0).
To go from the second quadrant to the fourth quadrant, the following transformations should occur:
1. **Reflect over the line y=0** (the x-axis): This reflection will take points in the second quadrant to the third quadrant. For example, a point (x, y) will be reflected to (x, -y). So a point in the second quadrant will move to the third quadrant.
2. **Reflect over the line x=0** (the y-axis): This reflection will take points from the third quadrant to the fourth quadrant. For example, a point (x, y) will be reflected to (-x, y), flipping the x-coordinate to negative.
3. **Reflect over the line y=x**: This transformation will swap the x and y coordinates of the shape, but in our case, the quadrilateral is already in place after the first two transformations.
Given these necessary reflections, we can see:
- The transformation sequence that reflects over the line y = 0 first would move ABCD to the third quadrant.
- The subsequent reflection over the line x = 0 would then move it to the fourth quadrant.
Now let's compare the given options:
**Option B**
> Reflect ABCD first over the line y=0, then over the line y=x.
In this option, the first reflection correctly takes ABCD to the third quadrant (which is not what we want) but does not help to get to EFGH.
**Option A**
> Reflect ABCD first over the line x=0, then over the line y=x.
This will not work because the first reflection takes the shape to the left instead of down.
**Option C**
> Reflect ABCD first over the line x=0, then over the line y=0.
This option does not correctly move the shape to the desired position either.
**Option D**
> Reflect ABCD over the line y=x.
This single reflection won't be sufficient to achieve the transformation needed.
Based on the analysis:
The **correct transformations** are achieved by reflecting ABCD **first over y=0 (the x-axis)**, then **over x=0 (the y-axis)**. This will correctly position ABCD transformed into EFGH.
Thus, the **correct response is**:
**Reflect ABCD first over the line y=0, then over the line y=x.**
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