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 rotating it 270° clockwise about the origin, we can use the rotation formula. A 270° clockwise rotation is equivalent to a 90° counter-clockwise rotation. The rotation formula for a point (x, y) to (x’, y’) is:
[ (x’, y’) = (y, -x) ]
Now, let’s rotate each of the triangle’s vertices:
1. For the point (-2, 1):
– New coordinates: (1, 2)
2. For the point (-6, 1):
– New coordinates: (1, 6)
3. For the point (-4, 5):
– New coordinates: (5, -4)
Putting these new coordinates together, we get the new vertices of the triangle as (1, 2), (1, 6), and (5, -4).
Among the provided options, the closest match is:
C (1, 2), (1, 6), and (4, 5)
However, please note that option C contains an error with the third coordinate (4, 5), which does not match our calculation. Therefore, none of the provided options are exactly correct based on the correct calculations.
Keep practicing and exploring these types of problems! If you need further assistance, feel free to reach out again.