To find the coordinates of point D′ after a 90° counterclockwise rotation about the origin, we can apply the following transformation to the coordinates (x, y) of point D:
- The new coordinates after a 90° counterclockwise rotation will be (-y, x).
Without knowing the original coordinates of point D (let's denote them as (x, y)), we can't directly compute D′. However, if we assume some possible coordinates for D, we can test each response option to see which one fits the transformation.
Here are the transformation calculations for each response option:
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If D originally had coordinates (x, y) where (x, y) results in (8, -4), we would have:
- x = -(-4) ⇒ y = 8
- Original point could be (4, 8).
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If D results in (4, -8), we would have:
- x = -(-8) ⇒ y = 4
- Original point could be (8, 4).
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If D results in (8, 4), we would have:
- x = -4 ⇒ y = 8
- Original point could thus be (4, 8).
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If D results in (-8, 4), we would have:
- x = -4 ⇒ y = -8
- Original point could thus be (-4, -8).
To find which of the provided options is consistent with the transformation for some point D, we need to find original coordinates that are plausible for a quadrilateral in the given constraints from -10 to 10 for both axes.
Since you ask for the coordinates of D′, we need the coordinate point after the rotation. So let's consider:
- A point like (4,8) would become (-8,4), and from the responses, this is one of the options.
Thus we can conclude that the coordinates for D′ in the options provided is:
(−8, 4).
So, the answer is:
(−8, 4).