Given the preimage coordinate (1, 8), what is the coordinate's x-value of the image after a counterclockwise rotation 90 degrees with the center of rotation at the origin (0,0)?

To find the new coordinate after a counterclockwise 90-degree rotation around the origin, we can use the following rule for rotating a point \((x, y)\) by 90 degrees counterclockwise:

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

Given the preimage coordinate \((1, 8)\), we apply the rotation rule:

\[
(x', y') = (-8, 1)
\]

So, the coordinate of the image after the rotation is \((-8, 1)\), and the **x-value** of this coordinate is \(-8\).

Would you like further explanation or details on how this rotation rule works?

Here are 5 related questions for further practice:
1. What is the y-value of the image after the same rotation?
2. What would be the coordinate after a 180-degree rotation of the point \((1, 8)\)?
3. How do you rotate a point 90 degrees clockwise around the origin?
4. What is the image of the point \((3, -5)\) after a 90-degree counterclockwise rotation?
5. How does the distance from the origin change after a rotation?

**Tip**: When rotating points around the origin, the distance from the origin (the magnitude of the vector) remains unchanged.

Learn how to find the x-value of the image after a 90-degree counterclockwise rotation of the point (1, 8) around the origin. This solution covers key concepts of coordinate geometry, including rotation transformations. Suitable for students in Grades 8-10.

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