What is the image of the point left parenthesis, minus, 2, comma, minus, 7, right parenthesis(−2,−7) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?

To determine the image of the point \((-2, -7)\) after a 90-degree counterclockwise rotation about the origin, we can apply the following transformation rule:

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

Here’s the process:
1. The original point is \((-2, -7)\).
2. After applying the rule:
   - \(x = -2\), \(y = -7\)
   - New coordinates: \((-(-7), -2)\) = \((7, -2)\)

Thus, the image of the point \((-2, -7)\) after a 90-degree counterclockwise rotation about the origin is **(7, -2)**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What would be the image of \((3, 5)\) after a 90-degree counterclockwise rotation?
2. How do you rotate a point 180 degrees about the origin?
3. What is the rule for a 90-degree clockwise rotation about the origin?
4. How do you find the new coordinates of a point after a 270-degree counterclockwise rotation?
5. What happens when you reflect a point across the x-axis?

**Tip:** For a 90-degree counterclockwise rotation, you simply switch the coordinates and change the sign of the original y-coordinate.

What is the image of the point (−2,−7) after a rotation of 90 degrees counterclockwise about the origin?

Learn how to find the image of the point (-2, -7) after a 90-degree counterclockwise rotation about the origin. This problem involves coordinate geometry and rotation transformation rules, suitable for students in Grades 9-10.

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