Rotate the point (−4, −6)

Question

on a geometric figure 90 degrees counterclockwise. What is the new point?

Answer 1

To rotate a point \((x, y)\) 90 degrees counterclockwise around the origin, you can use the following transformation:

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

For the point \((-4, -6)\):

1. Identify \(x\) and \(y\): \(x = -4\) and \(y = -6\).
2. Apply the transformation:
   • New \(x\) coordinate: \(-y = -(-6) = 6\)
   • New \(y\) coordinate: \(x = -4\)

So, the new point after a 90-degree counterclockwise rotation is:

\[ (6, -4) \]

Therefore, the new point is \((6, -4)\).