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.

Question

M' (___, ___)

Answer 1

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

\[ (x, y) \rightarrow (y, -x) \]

Now, applying this transformation to point \(M(0, 4)\):

1. Identify the coordinates of \(M\): \(x = 0\), \(y = 4\).
2. Apply the transformation:

\[ M' = (y, -x) = (4, -0) = (4, 0) \]

Therefore, the image of point \(M\) after the \(270^\circ\) rotation about the origin is:

\[ M' (4, 0) \]