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

(−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 \((x, y)\) counterclockwise by 270 degrees about the origin, you can use the following transformation formula:

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

Starting with the point \((5, 8)\):

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

Applying the transformation:

\[
(5, 8) \rightarrow (8, -5)
\]

Thus, the new point after rotating \((5, 8)\) 270 degrees counterclockwise about the origin is \((8, -5)\).

So the correct answer is:

\((8, -5)\)