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The problem describes a triangle \( LMN \) with the vertices \( L(0, 0) \), \( M(0, 4) \), and \( N(-3, 0) \). It asks for the coordinates of point \( N' \) after a 270° counterclockwise rotation around the origin.

To find the new coordinates of point \( N(-3, 0) \) after a 270° counterclockwise rotation about the origin, we apply the following transformation for a point \( (x, y) \):

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

For \( N(-3, 0) \):
- \( x = -3 \), and \( y = 0 \)
- Apply the transformation: 
  \[
  (x', y') = (0, -(-3)) = (0, 3)
  \]

Thus, the new coordinates for point \( N' \) are \( (0, 3) \).

The correct answer is **C. (0, 3)**.

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Would you like further details or have any other questions? Here are five related questions for additional practice:

1. What would be the coordinates of point \( M \) after a 270° counterclockwise rotation?
2. How does the rotation matrix for a 90° counterclockwise rotation compare to that of a 270° rotation?
3. What are the coordinates of point \( N' \) after a 180° rotation instead of 270°?
4. How do rotations around the origin affect the distances between points?
5. Can the same rotation transformation be applied to figures other than triangles? Why?

**Tip**: For any counterclockwise rotation by 270° around the origin, you can quickly swap the coordinates and negate the original \( x \)-coordinate to find the new point.

Triangle LMN has vertices at L(0, 0), M(0, 4), and N(−3, 0). The triangle will be rotated 270° counterclockwise about the origin. What will be the coordinates for point N'?

This problem explores how to find the coordinates of point N after rotating triangle LMN 270° counterclockwise about the origin. Learn the step-by-step process of applying the coordinate transformation formula for rotations, suitable for students in Grades 8-10.

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