Question
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A coordinate plane with 4 quadrants shows x and y axes ranging from negative 9 to 9 in increments of 1. Three rectangles are formed by lines joining four plotted points each. The coordinates of the plotted points for first rectangle joined by solid lines are left parenthesis negative 5 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 6 right parenthesis, and left parenthesis negative 5 comma negative 6 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 3 comma 4 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 5 comma 8 right parenthesis, and left parenthesis 3 comma 8 right parenthesis. The coordinates of the plotted points for the third rectangle joined by dotted lines are left parenthesis negative 4 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 5 right parenthesis, and left parenthesis negative 4 comma 5 right parenthesis.
The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. What is the next step?
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A coordinate plane with 4 quadrants shows x and y axes ranging from negative 9 to 9 in increments of 1. Three rectangles are formed by lines joining four plotted points each. The coordinates of the plotted points for first rectangle joined by solid lines are left parenthesis negative 5 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 6 right parenthesis, and left parenthesis negative 5 comma negative 6 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 3 comma 4 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 5 comma 8 right parenthesis, and left parenthesis 3 comma 8 right parenthesis. The coordinates of the plotted points for the third rectangle joined by dotted lines are left parenthesis negative 4 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 5 right parenthesis, and left parenthesis negative 4 comma 5 right parenthesis.
The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. What is the next step?
(1 point)
(
,
)
Remaining Attempts : 3
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Answers
Answered by
GPT-4o mini
To determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I after rotating the first rectangle 90 degrees clockwise about the origin, the next step is to translate the rotated rectangle to the same position as the rectangle in Quadrant I.
You would need to move the points of the rotated rectangle so they align with the corresponding points of the rectangle in Quadrant I.
In terms of coordinates, if the corners of the rectangle in Quadrant III after rotation are at specific coordinates, you would then translate them to match the corresponding coordinates of the rectangle in Quadrant I.
For example, if the coordinates after rotation were (x', y'), you would find the translation needed to match the coordinates of the points of the rectangle in Quadrant I.
Thus, the answer could posit that the next step is:
(Translate the rotated rectangle to align with the rectangle in Quadrant I)
You would need to move the points of the rotated rectangle so they align with the corresponding points of the rectangle in Quadrant I.
In terms of coordinates, if the corners of the rectangle in Quadrant III after rotation are at specific coordinates, you would then translate them to match the corresponding coordinates of the rectangle in Quadrant I.
For example, if the coordinates after rotation were (x', y'), you would find the translation needed to match the coordinates of the points of the rectangle in Quadrant I.
Thus, the answer could posit that the next step is:
(Translate the rotated rectangle to align with the rectangle in Quadrant I)