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

Question

(
5
,

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

(−5, 8)
(
−
5
,

8
)
left parenthesis negative 5 comma 8 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

(8, 5)

Answer 1

To find the new coordinates of a point \((x, y)\) after a rotation of 270 degrees counterclockwise about the origin, you can use the rotation transformation formula.

The general transformations for a rotation of a point \((x, y)\) are as follows:

• A 90-degree counterclockwise rotation transforms \((x, y)\) to \((-y, x)\).
• A 180-degree counterclockwise rotation transforms \((x, y)\) to \((-x, -y)\).
• A 270-degree counterclockwise rotation (or equivalently, a 90-degree clockwise rotation) transforms \((x, y)\) to \((y, -x)\).

Given the point \((5, 8)\), we apply the 270-degree rotation transformation:

1. Identify \(x = 5\) and \(y = 8\).
2. Apply the transformation: \[ (x, y) \rightarrow (y, -x) = (8, -5) \]

Thus, the new point after a 270-degree counterclockwise rotation about the origin is \((8, -5)\).

The correct response is \((8, -5)\).