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Parallelogram ABCD is rotated 90° counterclockwise. What rule shows the input and output of the rotation, and what is the new coordinate of A'?

a. (x,y)→(−x,−y);A′ is at(5,−1)
b. (x,y)→(−y,x);A′ is at(−1,−5)
c. (x,y)→(y,−x);A′ is at(1,5)
d. (x,y)→(x,−y);A′ is at(−5,−1)

User Lapis
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1 Answer

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Final answer:

The correct rotation rule for a 90° counterclockwise rotation of a parallelogram is (x, y) → (-y, x). Using this rule, point A would be transformed to new coordinates A', which is given as (-1, -5) in option b, assuming the original coordinates of A allow for this result after applying the transformation rule.

Step-by-step explanation:

The student asked about the rule for rotating a parallelogram 90° counterclockwise and the new coordinates for point A after the rotation. The correct transformation rule that applies to a 90° counterclockwise rotation is (x, y) → (-y, x), which effectively swaps the x and y values and changes the sign of the original y-value. Considering the rule and if the original coordinates of point A are known, we can apply this transformation to find the new location of A', which is denoted as point A'.

However, since the original coordinates of A are not provided, it is critical to determine the correct rule. Based on the provided choices, the correct one is option b. (x, y) → (-y, x). For this rotation, the y coordinate becomes the negative x coordinate, and the x coordinate becomes the positive y coordinate. Using the given options, option b also suggests that A' is at (-1, -5), assuming the original point A had coordinates which, when transformed using the given rule, would result in those coordinates for A'.

User DontPanic
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