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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 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)




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What is the capital of Egypt? ( Cairo )

1 Answer

  1. 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.

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