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 5 right parenthesis

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

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

(−5, 8)

Answer 1

To rotate a point (x, y) counterclockwise about the origin by 270 degrees, you can use the following transformation of coordinates:

1. Rotate 90 degrees counterclockwise: (x, y) → (-y, x)
2. Rotate 180 degrees counterclockwise: (x, y) → (-x, -y)
3. Rotate 270 degrees counterclockwise: (x, y) → (y, -x)

For the point (5, 8):

1. Rotate 270 degrees counterclockwise:
- New x-coordinate: y = 8
- New y-coordinate: -x = -5

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

Thus, the correct answer is:
**(8, -5)**.