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) left parenthesis negative 5 comma 9 right parenthesis

Answer 1

To rotate the point (9, 5) 270 degrees clockwise, you can use the following rule for rotation:

When rotating a point (x, y) 270 degrees clockwise:

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

Applying this to 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: \(-x = -9\)

So, (9, 5) rotated 270 degrees clockwise becomes:

\[
(5, -9)
\]

However, this does not match any of the answer choices directly. My apologies; let's go step by step:

Alternatively, a 270 degrees clockwise rotation can also be seen as a 90 degrees counterclockwise rotation.

The formula for a 90-degree counterclockwise rotation is:

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

Applying this to the point (9, 5):

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

Thus, (9, 5) rotated 270 degrees clockwise is:

\[
(-5, 9)
\]

So, the new point after the 270 degrees clockwise rotation is \(\text{(−5, 9)}\).