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

Answer 1

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

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

In this case, the point is \((5, 8)\). Plugging these values into the formula gives:

\[
(x', y') = (8, -5)
\]

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

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