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.