To find the image of the point $(-1, 7)$ after a 90° counterclockwise rotation about the origin, we can use the standard rotation rule for rotating a point $(x, y)$ by 90° counterclockwise:

$(x', y') = (-y, x)$

For the point $(-1, 7)$:

• The x-coordinate becomes $-7$,
• The y-coordinate becomes $-1$.

Thus, the new coordinates after the rotation are:

$\text{New point} = (-7, -1)$

The image of the point $(-1, 7)$ after a 90° counterclockwise rotation is $(-7, -1)$.

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Would you like further details on this rotation process or any clarifications?

Related Questions:

1. What is the general formula for rotating a point by different angles?
2. How does the rotation change if it were clockwise instead?
3. Can you explain how to rotate a point around a point other than the origin?
4. How do you determine the distance between the original and rotated points?
5. What would happen if the point $(-1, 7)$ is reflected across the x-axis instead of rotated?

Tip: When rotating points, always visualize how the axes change and apply the correct transformation rule.