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A quadrilateral with vertices G(-10, 1)

, E(-6, -4), O(2,0), and M(0, 4) is rotated about the origin 270 degrees (counterclockwise). Apply rotation mapping rules to find the image of M.
(1 point)
M'(

1 answer

To rotate a point \((x, y)\) about the origin by \(270^\circ\) counterclockwise, we can use the rotation transformation formula:

\[ (x', y') = (y, -x) \]

For point \(M(0, 4)\), we apply the formula:

  1. Identify \(x\) and \(y\) values from point \(M\):

    • \(x = 0\)
    • \(y = 4\)

  2. Apply the rotation transformation:

    • \(x' = y = 4\)
    • \(y' = -x = -0 = 0\)

Thus, the image of point \(M\) after rotating \(270^\circ\) counterclockwise about the origin is:

\[ M' = (4, 0) \]

So, the answer is:

M' (4, 0)