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 negative 8 comma negative 5 right parenthesis (−5, 8) left parenthesis negative 5 comma 8 right parenthesis (8, 5) left parenthesis 8 comma 5 right parenthesis (8, −5)

Answer 1

To rotate a point \( (x, y) \) 270 degrees counterclockwise about the origin, you can use the rotation transformation formula:

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

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

1. \( x' = y = 8 \)
2. \( y' = -x = -5 \)

So, rotating \( (5, 8) \) 270 degrees counterclockwise about the origin gives us the new point:

\[
(8, -5)
\]

Thus, the answer is \( \boxed{(8, -5)} \).