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

Question

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.