A line segment has endpoints (−2, 4)

Question

and (1, 5)
. What are the endpoints after a 90° counterclockwise rotation

Answer 1

To perform a 90° counterclockwise rotation of a point around the origin, you can use the following transformation:

If a point has coordinates \((x, y)\), after a 90° counterclockwise rotation, the new coordinates \((x', y')\) will be given by: \[ (x', y') = (-y, x) \]

Let's compute the new coordinates for the endpoints of the line segment given the points \((-2, 4)\) and \((1, 5)\):

1. For the first endpoint \((-2, 4)\):

   • \(x' = -y = -4\)
   • \(y' = x = -2\)
   • So the new coordinates are \((-4, -2)\).

2. For the second endpoint \((1, 5)\):

   • \(x' = -y = -5\)
   • \(y' = x = 1\)
   • So the new coordinates are \((-5, 1)\).

After the 90° counterclockwise rotation, the new endpoints of the line segment are \((-4, -2)\) and \((-5, 1)\).