Question

What is the new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin?(1 point) Responses (8, −5) left parenthesis 8 comma negative 5 right parenthesis (−8, −5) left parenthesis negative 8 comma negative 5 right parenthesis (8, 5) left parenthesis 8 comma 5 right parenthesis (−5, 8)

Answer 1

To rotate a point \((x, y)\) around the origin by \(270^\circ\) counterclockwise, you can use the following rotation formula:

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

For the point \((5, 8)\):

1. Set \(x = 5\) and \(y = 8\).
2. Apply the rotation formula:
   • \(x' = y = 8\)
   • \(y' = -x = -5\)

Thus, the new coordinates after rotation are \((8, -5)\).

So the correct answer is \((8, -5)\).