Question

Rotate the point (9, 5)
on a geometric figure 270 degrees clockwise. What is the new point?(1 point)
Responses

(5, 9)

left parenthesis 5 comma 9 right parenthesis
(−5,−9)
left parenthesis negative 5 comma negative 9 right parenthesis
(−9,−5)
left parenthesis negative 9 comma negative 5 right parenthesis
(−5, 9)

Answer 1

To rotate a point \((x, y)\) 270 degrees clockwise, you can use the rotation transformation formula:

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

For the point \((9, 5)\):

1. The new x-coordinate will be the original y-coordinate: \(y = 5\).
2. The new y-coordinate will be the negative of the original x-coordinate: \(-x = -9\).

Thus, the new point after a 270-degree clockwise rotation is:

\[
(5, -9)
\]

However, it appears that I made a mistake because \( (-5, 9) \) corresponds to a 90 degrees clockwise rotation.

To correct this, let's derive the 270 degrees clockwise rotation step-by-step correctly:

1. The transformation for a 270-degree clockwise rotation (also equivalent to a 90-degree counterclockwise rotation) is:
\[
(x, y) \rightarrow (-y, x)
\]

For the point \((9, 5)\):

- The new x-coordinate will be \(-y = -5\).
- The new y-coordinate will be \(x = 9\).

So the new point after a 270-degree clockwise rotation is:

\[
(-5, 9)
\]

Hence, the correct response is \((-5, 9)\).