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 .

Answer 1

To rotate a point \((x, y)\) counterclockwise around the origin by \(270^\circ\), we can use the rotation mapping rules. The rule for a rotation of \(270^\circ\) counterclockwise is given by the transformation:

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

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

1. Identify the coordinates:

   • The coordinates of point \(M\) are \(x = 0\) and \(y = 4\).

2. Apply the rotation mapping:

   • According to the mapping, we swap \(x\) and \(y\) and change the sign of the original \(x\): \[ (0, 4) \rightarrow (4, -0) \]

3. Simplify the coordinates: \[ (4, 0) \]

Thus, the image of point \(M\) after a \(270^\circ\) counterclockwise rotation about the origin is \((4, 0)\).