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 find the new coordinates of the point (5, 8) after a 270-degree counterclockwise rotation around the origin, we can use the following transformation rules for rotations:

- A 90-degree counterclockwise rotation transforms a point (x, y) to (-y, x).
- A 180-degree rotation transforms a point (x, y) to (-x, -y).
- A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation, which transforms (x, y) to (y, -x).

Applying the 270-degree rotation to the point (5, 8):
- The new coordinates will be (y, -x) = (8, -5).

Therefore, the new point is **(8, -5)**.