Rotate the point (9, 5)

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

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

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

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

(−5, 9)

1 answer

To rotate the point \((9, 5)\) by 270 degrees clockwise, you can think of this as a 90 degrees counterclockwise rotation. The formulas for rotation are:

  • For 90 degrees counterclockwise: \((x, y) \rightarrow (-y, x)\)
  • For 270 degrees clockwise: \((x, y) \rightarrow (y, -x)\)

Let's apply the 270 degrees clockwise (or 90 degrees counterclockwise) rotation to the point \((9, 5)\):

Using the transformation \((x, y) \rightarrow (y, -x)\),

  • \(x = 9\)
  • \(y = 5\)

Now applying the transformation: \[ (9, 5) \rightarrow (5, -9) \]

The new point after a 270 degrees clockwise rotation is \((5, -9)\).

Since this point is not in your response options, it appears there may be a misunderstanding in either the provided options or the math. Please verify the options again:

Based on the standard rotation rules, if you were to additionally check:

  • (−9,−5)
  • (5,9)
  • (−5,−9)
  • (−5,9)

None of them match \((5, -9)\), suggesting that there might be confusion.

For clarity: A 270-degree clockwise rotation of \((9,5)\) should yield \((5,-9)\). Please check your options again, or let me know if you'd like further assistance!