(3,3) rotated 90 degrees counterclockwise around the origin

Answer 1

To rotate a point counterclockwise around the origin by 90 degrees, you can use the rotation formula:

If you have a point \((x, y)\), after a 90-degree counterclockwise rotation, the new coordinates \((x', y')\) will be given by:

\[ (x', y') = (-y, x) \]

For the point \((3, 3)\):

1. Identify \(x\) and \(y\):

   • \(x = 3\)
   • \(y = 3\)

2. Apply the rotation formula: \[ x' = -y = -3 \] \[ y' = x = 3 \]

Thus, after rotating the point \((3, 3)\) 90 degrees counterclockwise around the origin, the new coordinates will be \((-3, 3)\).