A quadrilateral with vertices G(-8,2), E(-5,3), O(3,0), and M(6.0) is rotated about the origin 270 degrees (counterclockwise). Apply rotation mapping rules to find the image of M.(2 points)

Question

M(,)
6
-6
0
-5
5
3
-3

Answer 1

To rotate a point \((x, y)\) about the origin by 270 degrees counterclockwise, we can use the rotation mapping rules, which transform the point as follows:

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

For the point \(M(6, 0)\):

1. Substitute \(x = 6\) and \(y = 0\) into the transformation:
   • New \(x\) coordinate: \(y = 0\)
   • New \(y\) coordinate: \(-x = -6\)

Thus, the image of point \(M(6, 0)\) after a 270-degree counterclockwise rotation about the origin is:

\[ M' (0, -6) \]

So, the final coordinates of the image of \(M\) after rotation are:

\[ M'(0, -6) \]