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To find the image of point \( M(0, 4) \) after a rotation of 270 degrees counterclockwise about the origin, we use the following rule for rotation:

- A 270° counterclockwise rotation is the same as a 90° clockwise rotation.
- The mapping rule for a 270° counterclockwise rotation is: 
  \[
  (x, y) \rightarrow (y, -x)
  \]

Now, let's apply this rule to the point \( M(0, 4) \):

\[
M(0, 4) \rightarrow (4, 0)
\]

Thus, the coordinates of \( M' \), the image of \( M \), after the rotation are \( M'(4, 0) \).

Would you like more details on the rotation process or have any questions?

Here are 5 related questions to expand on the topic:
1. What is the rule for a 90° counterclockwise rotation about the origin?
2. How would the image of point \( G(-10, 1) \) change under a 270° counterclockwise rotation?
3. Can you explain how to rotate a point 180 degrees about the origin?
4. What is the effect of rotating a point by 360° about the origin?
5. How would the image of point \( E(-6, -4) \) change after a 270° counterclockwise rotation?

**Tip:** For rotations, remember that a 270° counterclockwise rotation is equivalent to a 90° clockwise rotation!

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.

Learn how to apply the rotation mapping rule to find the image of point M(0, 4) after a 270° counterclockwise rotation about the origin. This problem is ideal for students in Grades 8-10 and covers key concepts in geometry, such as rotation and coordinate transformations.

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