Write the coordinate notation to describe the following rotation from J(2.6,1) to J'(-2.6,-1).

(x,y)→(-x,-y)

(x,y)→(-y,x)

(x,y)→(y,-x)

(x,y)→(-y,-x)

The problem involves determining the correct coordinate notation for the rotation that maps point \( J(2.6, 1) \) to point \( J'(-2.6, -1) \).

Looking at the transformation from \( J(2.6, 1) \) to \( J'(-2.6, -1) \), the coordinates are both negated and switched sign, which suggests this is a 180-degree rotation around the origin.

The correct coordinate notation for a 180-degree rotation is:

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

Thus, the correct answer is: 
\[
(x, y) \rightarrow (-x, -y)
\]

Do you need further details on this transformation, or have any questions?

Here are 5 relative questions based on this topic:
1. What is the rule for a 90-degree clockwise rotation around the origin?
2. How would the point \( A(3, 4) \) transform under a 270-degree rotation around the origin?
3. What is the general formula for rotating a point \( (x, y) \) by 90 degrees counterclockwise?
4. How do you determine the angle of rotation from a given transformation?
5. Can you explain how reflections differ from rotations in terms of coordinate transformations?

**Tip**: A 180-degree rotation is equivalent to reflecting a point across both the x-axis and y-axis simultaneously.

Write the coordinate notation to describe the following rotation from J(2.6,1) to J'(-2.6,-1).

Explore the coordinate transformation for a 180-degree rotation, where point J(2.6, 1) is rotated to J'(-2.6, -1). Understand key geometric concepts, including the rotation theorem and transformations in coordinate geometry. Suitable for students in Grades 9-10.

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