A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? Enter the number of the correct option.

Question

Option #1: (x,y)→(y,−x)

Option #2: (x,y)→(−y,x)

Option #3: (x,y)→(−x,−y)

Option #4: (x,y)→(y,x)

(1 point)
The mapping for a 90-degree counterclockwise rotation is Option #
.
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Answer 1

The correct mapping for a 90-degree counterclockwise rotation about the origin is:

Option #1: (x,y)→(−y,x)

So, the answer is Option #2.

Answer 2

are you sure?

Answer 3

I apologize for the confusion in my previous response. To clarify:

For a 90-degree counterclockwise rotation about the origin, the correct transformation of the point \((x, y)\) is:

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

So the correct answer is Option #2: (x, y) → (-y, x).

Thank you for your patience!

Answer 4

Provide two different degrees of rotation less than 75° but greater than 0° that will turn a regular dodecagon onto itself.(1 point)
A regular dodecagon will turn onto itself after a
° and
° rotation.

Answer 5

A regular dodecagon has 12 sides. It can be rotated onto itself by multiples of \(\frac{360°}{12} = 30°\).

To find two different degrees of rotation less than 75° but greater than 0°, we can consider the following multiples of 30°:

1. 30°
2. 60°

Therefore, a regular dodecagon will turn onto itself after a 30° and a 60° rotation.

Answer 6

A circle measures 360 degrees. If this circle were marked with numbers like a clock, every number would represent 30 degrees farther from 0 and closer to 360 degrees. If an angle marker typically found at 11:00 were to rotate to the place normally marked for 4:00, what is the degree measure of the angle formed moving clockwise?

(1 point)
Responses

150 degrees
150 degrees

120 degrees
120 degrees

240 degrees
240 degrees

330 degrees

Answer 7

To find the degree measure of the angle formed by rotating from the position of 11:00 to the position of 4:00 on a clock, we can calculate the following:

1. Determine the positions of the numbers:

   • 11:00 is at \(11 \times 30° = 330°\)
   • 4:00 is at \(4 \times 30° = 120°\)

2. Calculate the angle moving clockwise from 11:00 to 4:00:

   • Starting at 330°, moving clockwise to 120° means you pass 360° and return to 0° before reaching 120°.
   • The angle can be calculated as: \[ \text{Angle} = 360° - 330° + 120° = 30° + 120° = 150° \]

Thus, the degree measure of the angle formed moving clockwise is 150 degrees.