Question

What is the new point when you rotate a geometric figure with point (5, 8)
(
5
,

8
)
270 degrees counterclockwise about the origin?(1 point)
Responses

(8, 5)
(
8
,

5
)
left parenthesis 8 comma 5 right parenthesis

(8, −5)
(
8
,

−
5
)
left parenthesis 8 comma negative 5 right parenthesis

(−8, −5)
(
−
8
,

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

(−5, 8)
(
−
5
,

8
)
left parenthesis negative 5 comma 8 right parenthesis

Answer 1

To rotate a point \((x, y)\) by \(270^\circ\) counterclockwise about the origin, you can use the transformation rule:

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

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

1. Substitute \(x = 5\) and \(y = 8\) into the transformation:
\[
(5, 8) \to (8, -5)
\]

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

Therefore, the correct answer is:

\((8, -5)\)