rotation 270° clockwise about the origin Z(−1, −5), K(−1, 0), C(1, 1),N(3, −2)

To rotate each point 270° clockwise (or equivalently, 90° counterclockwise) about the origin, we apply the rotation transformation rules for 90° counterclockwise:

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

Let's apply this rule to each point:

1. **Point \( Z(-1, -5) \):**
   - Rotation: \( (-y, x) \Rightarrow (-(-5), -1) = (5, -1) \)
   - New coordinates: \( Z' = (5, -1) \)

2. **Point \( K(-1, 0) \):**
   - Rotation: \( (-y, x) \Rightarrow (0, -1) \)
   - New coordinates: \( K' = (0, -1) \)

3. **Point \( C(1, 1) \):**
   - Rotation: \( (-y, x) \Rightarrow (-1, 1) \)
   - New coordinates: \( C' = (-1, 1) \)

4. **Point \( N(3, -2) \):**
   - Rotation: \( (-y, x) \Rightarrow (2, 3) \)
   - New coordinates: \( N' = (2, 3) \)

### Summary of Rotated Points:
- \( Z' = (5, -1) \)
- \( K' = (0, -1) \)
- \( C' = (-1, 1) \)
- \( N' = (2, 3) \)

Would you like a visual representation or further explanation of the rotation process?

Here are some follow-up questions to deepen your understanding:

1. What would be the result of rotating the points by 90° clockwise?
2. How would a 180° rotation affect the coordinates of each point?
3. How would the coordinates change with a translation after the rotation?
4. How is rotating about a point different from rotating about the origin?
5. How can you generalize the rotation formula for any angle?

**Tip:** For rotations, remember that a 270° clockwise rotation is the same as a 90° counterclockwise rotation.

Explore how to rotate the points Z(-1, -5), K(-1, 0), C(1, 1), and N(3, -2) 270° clockwise about the origin. This guide provides a step-by-step solution using the 90° counterclockwise rotation rule, which is equivalent to the 270° clockwise rotation. Suitable for students in Grades 8-10.

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