Question

(-4,-9) to (-9,4) rotation type

is it 90 degrees counterclockwise??

Answer 1

To determine the type of rotation from the point \((-4, -9)\) to \((-9, 4)\), we can follow these steps:

1. **Calculate the center of rotation**: If we assume a standard rotation around the origin (0,0), we'll need to see how the coordinates change from the first point to the second.

2. **Visualize the points**:
- The original point is \((-4, -9)\).
- The new point is \((-9, 4)\).

3. **Check the change in coordinates**:
- The point \((-4, -9)\) can be plotted. Moving to \((-9, 4)\) involves both a change in the x-coordinate and y-coordinate.

4. **Rotation logic**:
- A 90-degree counterclockwise rotation around the origin (0, 0) transforms the point \((x, y)\) to \((-y, x)\).
- Let's check if \((-4, -9)\) under a 90-degree counterclockwise rotation results in \((-9, 4)\):
- Starting with \((-4, -9)\):
- \((-y, x) \rightarrow (9, -4)\) (which is not \((-9, 4)\)).

5. **Calculation for a different point**:
- A 180-degree rotation transforms \((x,y)\) to \((-x,-y)\).
- \((-4, -9)\) under a 180-degree rotation becomes \((4, 9)\).

6. **Determining final relation**:
- It’s clear that the transformation does not fit 90 degrees or 180 degrees centered at the origin.

There's also a possibility it could be rotated around a point other than the origin, but given just two points, we cannot assign a specific rotation angle directly with the information provided.

**Conclusion**: The rotation from \((-4, -9)\) to \((-9, 4)\) is not a 90-degree counterclockwise rotation around the origin. The exact angle or axis of rotation is not determined from this simple analysis alone. Analyzing the coordinates yields a different transformation.