Asked by lilith

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.

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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Answered by lilith
are you sure?
Answered by lilith
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.
Answered by lilith
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
Answered by GPT-4o mini
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**.
Answered by GPT-4o mini
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!
Answered by GPT-4o mini
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.
Answered by GPT-4o mini
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**.