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Use the image to answer the question. An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6...Question
Question
Use the image to answer the question.
An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Eight points are plotted on the plane. Two quadrilaterals are graphed on the plane. Four points are plotted in the first quadrant. Point A is plotted at the coordinates left parenthesis 3 comma 6 right parenthesis, Point B is plotted at left parenthesis 3 comma 2 right parenthesis, point C is plotted at left parenthesis 6 comma 2 right parenthesis, and point D is plotted at left parenthesis 5 comma 6 right parenthesis. Points A and B, points B and C, points C and D, and points D and A are connected by dotted line segments to form quadrilateral A B C D. Four unlabeled points are plotted in the second quadrant at the coordinates left parenthesis negative 2 comma 6 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 5 comma 2 right parenthesis, and left parenthesis negative 4 comma 6 right parenthesis. The four points are connected by line segments to form a quadrilateral.
Your friend produced a reflection over the y
-axis that looks like this figure. You notice a problem with the reflection. How would you suggest correcting the reflection?
(1 point)
Responses
Shift the reflected figure 1 unit to the right.
Shift the reflected figure 1 unit to the right.
Shift the reflected figure 1 unit to the left.
Shift the reflected figure 1 unit to the left.
Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit down.
Shift the reflected figure 1 unit down.
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Use the image to answer the question.
An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Eight points are plotted on the plane. Two quadrilaterals are graphed on the plane. Four points are plotted in the first quadrant. Point A is plotted at the coordinates left parenthesis 3 comma 6 right parenthesis, Point B is plotted at left parenthesis 3 comma 2 right parenthesis, point C is plotted at left parenthesis 6 comma 2 right parenthesis, and point D is plotted at left parenthesis 5 comma 6 right parenthesis. Points A and B, points B and C, points C and D, and points D and A are connected by dotted line segments to form quadrilateral A B C D. Four unlabeled points are plotted in the second quadrant at the coordinates left parenthesis negative 2 comma 6 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 5 comma 2 right parenthesis, and left parenthesis negative 4 comma 6 right parenthesis. The four points are connected by line segments to form a quadrilateral.
Your friend produced a reflection over the y
-axis that looks like this figure. You notice a problem with the reflection. How would you suggest correcting the reflection?
(1 point)
Responses
Shift the reflected figure 1 unit to the right.
Shift the reflected figure 1 unit to the right.
Shift the reflected figure 1 unit to the left.
Shift the reflected figure 1 unit to the left.
Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit down.
Shift the reflected figure 1 unit down.
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Answers
GPT-4o mini
To analyze the reflection over the y-axis of the quadrilateral A B C D and its corresponding points, we need to apply the rules for reflecting points across the y-axis.
The coordinates of the points before reflection are as follows:
- Point A: (3, 6) → Reflects to (-3, 6)
- Point B: (3, 2) → Reflects to (-3, 2)
- Point C: (6, 2) → Reflects to (-6, 2)
- Point D: (5, 6) → Reflects to (-5, 6)
Now, when we reflect the points in the second quadrant (let's denote them as points E, F, G, and H):
- Point E: (-2, 6) → Reflects to (2, 6)
- Point F: (-2, 2) → Reflects to (2, 2)
- Point G: (-5, 2) → Reflects to (5, 2)
- Point H: (-4, 6) → Reflects to (4, 6)
Next, if the reflected figure does not appear in the correct position after this process, we need to determine the nature of the error.
If the reflection appears to be in the wrong position, we can check where it should be. For the points in the second quadrant initially, if they are supposed to be transformed correctly, they should fall into the first quadrant after reflecting over the y-axis.
The most likely correction needed for a misalignment (where points should be due to reflection) would typically involve a shift. Given the coordinates of the reflected points, if they appear close to the zero mark but are not accurately represented after reflection, logically we would need to adjust their horizontal positions.
If the entire reflected figure appears shifted to the left compared to where it should align with newly reflected points, we would suggest shifting the reflected figure 1 unit to the right to correct the alignment.
Thus, the correct response to suggest correcting the reflection is:
**Shift the reflected figure 1 unit to the right.**
The coordinates of the points before reflection are as follows:
- Point A: (3, 6) → Reflects to (-3, 6)
- Point B: (3, 2) → Reflects to (-3, 2)
- Point C: (6, 2) → Reflects to (-6, 2)
- Point D: (5, 6) → Reflects to (-5, 6)
Now, when we reflect the points in the second quadrant (let's denote them as points E, F, G, and H):
- Point E: (-2, 6) → Reflects to (2, 6)
- Point F: (-2, 2) → Reflects to (2, 2)
- Point G: (-5, 2) → Reflects to (5, 2)
- Point H: (-4, 6) → Reflects to (4, 6)
Next, if the reflected figure does not appear in the correct position after this process, we need to determine the nature of the error.
If the reflection appears to be in the wrong position, we can check where it should be. For the points in the second quadrant initially, if they are supposed to be transformed correctly, they should fall into the first quadrant after reflecting over the y-axis.
The most likely correction needed for a misalignment (where points should be due to reflection) would typically involve a shift. Given the coordinates of the reflected points, if they appear close to the zero mark but are not accurately represented after reflection, logically we would need to adjust their horizontal positions.
If the entire reflected figure appears shifted to the left compared to where it should align with newly reflected points, we would suggest shifting the reflected figure 1 unit to the right to correct the alignment.
Thus, the correct response to suggest correcting the reflection is:
**Shift the reflected figure 1 unit to the right.**