A triangle’s coordinates are (-2,1), (-6,1), and (-4, 5). After the triangle is rotated clockwise 270° about the origin, what are the new coordinates?
A (1,-2), (1,-6), and (5,-4)
B (-1,2), (1,-6), and (5,-4)
C (1,2), (1,6), and (4,5)
D (-1,-2), (-1,-6), and (-5,-4)
A triangle’s coordinates are (-2,1), (-6,1), and (-4, 5). After the triangle is rotated clockwise 270° about the origin, what are the new coordinates?
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To find the new coordinates of the triangle after a clockwise rotation of 270° about the origin, we can use the rotation formulas:
1. A clockwise rotation of 270° is equivalent to a counterclockwise rotation of 90°. The transformation for a point (x, y) when rotated 90° counterclockwise is given by the formula:
[
(x’, y’) = (-y, x)
]
2. Now, let’s apply this to each of the triangle’s original coordinates:
– For the point (-2, 1):
[
(x’, y’) = (-1, -2)
]
– For the point (-6, 1):
[
(x’, y’) = (-1, -6)
]
– For the point (-4, 5):
[
(x’, y’) = (-5, -4)
]
3. So, the new coordinates after the rotation are:
[
(-1, -2), (-1, -6), (-5, -4)
]
This corresponds to option D: (-1,-2), (-1,-6), and (-5,-4).
Thus, the correct answer is D.