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





To rotate each of the points \( Z(-1, -5) \), \( K(-1, 0) \), \( C(1, 1) \), and \( N(3, -2) \) by \(270^\circ\) clockwise about the origin, we’ll use the rule for a \(270^\circ\) clockwise rotation. For any point \((x, y)\), rotating it \(270^\circ\) clockwise about the origin transforms it to the point \((y, -x)\).

Let’s apply this transformation to each point:

1. **Point \( Z(-1, -5) \):**
   - After rotation: \((-5, 1)\)

2. **Point \( K(-1, 0) \):**
   - After rotation: \((0, 1)\)

3. **Point \( C(1, 1) \):**
   - After rotation: \((1, -1)\)

4. **Point \( N(3, -2) \):**
   - After rotation: \((-2, -3)\)

### Final Coordinates After \(270^\circ\) Clockwise Rotation:
- \( Z' = (-5, 1) \)
- \( K' = (0, 1) \)
- \( C' = (1, -1) \)
- \( N' = (-2, -3) \)

Would you like a step-by-step explanation of the transformation process, or is there anything specific you want to clarify?

### Additional Related Questions:
1. How does a \(270^\circ\) clockwise rotation differ from a \(90^\circ\) counterclockwise rotation?
2. How would the coordinates change if we used a different center of rotation?
3. What is the effect of rotating these points \(180^\circ\) clockwise instead?
4. Could you calculate the distance between each original and rotated point?
5. How can we apply matrix multiplication to perform this rotation?

#### Tip:
For any \(270^\circ\) clockwise rotation, simply switch \(x\) and \(y\), then make \(x\) negative for the new coordinates.

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

Learn how to apply a 270° clockwise rotation to points in the coordinate plane, such as Z(−1, −5), K(−1, 0), C(1, 1), and N(3, −2). This solution explains the step-by-step process and the resulting coordinates after transformation. Suitable for students in Grades 9-12.

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