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.