Question

A triangle is rotated about P in the diagram. Complete the sentence to accurately describe the degree of rotation in both directions. Recall that clockwise rotations are written with a negative degree.

(1 point)
The triangle is rotated
° counterclockwise about P or
° clockwise about P

Answer 1

Identify the degree of rotation in both directions for the pictured rectangle, centered about the point (1,0) . Recall that clockwise rotations are denoted with a negative degree.

(1 point)
The quadrilateral is rotated
° counterclockwise or
° clockwise.

Answer 2

Use the image of the uppercase letter to describe the rotation that would turn the image so that it appears the same. Enter the number that corresponds to your answer.

1) 90° clockwise rotation

2) 90° counterclockwise rotation

3) 180° counterclockwise rotation

4) 270° counterclockwise rotation

(1 point)
Perform a
and the letter will look the same as the original.

Answer 3

thats wrong

Answer 4

P(−7,2) is rotated 270° (counterclockwise) about the origin. Name the quadrant P′ is located in. Enter the option number that corresponds to your answer.

Option #1: Quadrant I

Option #2: Quadrant II

Option #3: Quadrant III

Option #4: Quadrant IV

(1 point)
P′ is located in Option #
.
Remaining

Answer 5

Trapezoid DEFG has vertices D(1,3) , E(5,3) , F(7,−1) and G(1,−1) . Imagine the image D′E′F′G′ after a 90° (counterclockwise) rotation about the origin. Enter the coordinate of E′ .

(1 point)
E′ is located at (
,
).

Answer 6

To complete the sentence accurately, I would need the specific degree of rotation indicated in the diagram. Since I can't see the diagram, I'll provide a generic template.

For example:

If the triangle is rotated 90 degrees counterclockwise and 90 degrees clockwise, you can fill in the blanks as follows:

The triangle is rotated **90° counterclockwise** about P or **-90° clockwise** about P.

Replace the degrees in the sentence with the specific rotation values from your diagram.

Answer 7

Since I cannot see the specific rectangle and its rotation in your diagram, I'll provide you with a general format to fill in the degrees based on what you observe in the picture.

1. Let's say the rectangle is rotated **30 degrees** counterclockwise and therefore would be rotated **-30 degrees** clockwise.

Here’s how you would fill it in:

The quadrilateral is rotated **30° counterclockwise** or **-30° clockwise**.

If the rotation in your specific case is different, just replace "30" with the correct degree of rotation based on your diagram.

Answer 8

To determine how to rotate the uppercase letter so that it appears the same, we need to consider the symmetries of the letter.

For most uppercase letters:

1. **90° clockwise rotation**: The letter will change appearance significantly.
2. **90° counterclockwise rotation**: The letter will change appearance significantly.
3. **180° counterclockwise rotation**: The letter will look the same for symmetric letters like "O," "S," "H," "I," and some others.
4. **270° counterclockwise rotation** (which is equivalent to a 90° clockwise rotation): The letter will change appearance significantly.

If the letter in question is one of those that maintains its appearance after a 180° rotation (like "O," "S," or "H"), the correct answer would be:

**Perform a 180° counterclockwise rotation and the letter will look the same as the original.**

If the letter is not among those that look the same after such a rotation, you may need to adjust the answer according to the specific letter you are considering.

Answer 9

I apologize for any confusion in my previous response. Without the specific letter or its orientation, it's challenging to provide a definitive answer.

For common uppercase letters:

- **"O"**: Looks the same after any rotation (90°, 180°, 270°).
- **"H"**: Looks the same after 180° and 0° rotation.
- **"I"**: Looks the same after any rotation.
- **"S"**: Looks the same after 180° rotation but not 90° or 270°.
- **"X"**: Looks the same after any rotation.

If you're trying to identify the rotation that makes a specific letter appear the same, the correct answer should be based on that specific letter.

If you can specify the letter in question, I can better guide you on what rotation will keep it looking the same. Otherwise, considering your feedback, I recommend using a 90° or 270° rotation if the letter is symmetrical in that manner (like "N" or "Z").

Please let me know the letter so I can assist you more accurately.

Answer 10

To find the new location of the point \( P(-7, 2) \) after a 270° counterclockwise rotation about the origin, we can use the rotation transformation formulas.

**Rotation Formula for 270° Counterclockwise:**
When a point \( (x, y) \) is rotated 270° counterclockwise, the new coordinates \( (x', y') \) are given by:
\[
(x', y') = (y, -x)
\]

**Applying the formula to point \( P(-7, 2) \):**
- \( x = -7 \)
- \( y = 2 \)

Now apply the rotation:
\[
(x', y') = (2, -(-7)) = (2, 7)
\]

Now we need to determine the quadrant of the new point \( P'(2, 7) \):
- Since the x-coordinate is positive (2) and the y-coordinate is positive (7), this point lies in **Quadrant I**.

Thus, the answer is:

**P′ is located in Option #1.**

Answer 11

To find the coordinates of point \( E' \) after a 90° counterclockwise rotation about the origin, we can use the rotation transformation formula.

**Rotation Formula for 90° Counterclockwise:**
When a point \( (x, y) \) is rotated 90° counterclockwise, the new coordinates \( (x', y') \) are given by:
\[
(x', y') = (-y, x)
\]

**Applying the formula to point \( E(5, 3) \):**
- \( x = 5 \)
- \( y = 3 \)

Now apply the rotation:
\[
(x', y') = (-3, 5)
\]

Thus, the coordinates of \( E' \) after the 90° counterclockwise rotation about the origin are:

**E′ is located at (-3, 5).**