Question

The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?(1 point)
Responses

a translation
a translation

a dilation with a scale factor of 14
a dilation with a scale factor of Start Fraction 1 over 2 End Fraction

a 270 degrees counterclockwise rotation
a 270 degrees counterclockwise rotation

a reflection over the line y=x



A vertex of △PQR is rotated from Q(−4,−9) to Q′(−9,4) . Use rotation function mapping to determine where the image of the other two vertices P(−4,0) and R(4,−4) , should be placed.(1 point)
Responses

P′(0,−4) and R′(−4,4)
upper P prime left parenthesis 0 comma negative 4 right parenthesis and upper R left parenthesis negative 4 comma 4 right parenthesis

P′(0,4) and R′(−4,−4)
upper P prime left parenthesis 0 comma 4 right parenthesis and upper R left parenthesis negative 4 comma negative 4 right parenthesis

P′(0,4) and R′(−4,4)
upper P prime left parenthesis 0 comma 4 right parenthesis and upper R left parenthesis negative 4 comma 4 right parenthesis

P′(0,−4) and R′(−4,−4)




A point is rotated about the origin. Its coordinates are P(−4,10) and P′(−10,−4). Determine the degree of rotation and direction by applying rotation mapping.(1 point)
Responses

−180 degrees (clockwise) or 180 degrees (counterclockwise)
negative 180 degrees (clockwise) or 180 degrees (counterclockwise)

270 degrees (counterclockwise)
270 degrees (counterclockwise)

90 degrees (counterclockwise)
90 degrees (counterclockwise)

−90 degrees (clockwise)




Which of the following mappings is used for a 270-degree (counterclockwise) rotation?(1 point)
Responses

(x,y)→(−y,x)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma x right parenthesis

(x,y)→(−x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis

(x,y)→(−y,−x)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma negative x right parenthesis

(x,y)→(y,−x)

Answer 1

Let's go through each question one by one:

1. **The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?**

The correct response is: **a 270 degrees counterclockwise rotation.**
(A 90-degree clockwise rotation is equivalent to a 270-degree counterclockwise rotation.)

2. **Determine where the image of the other two vertices P(−4,0) and R(4,−4) should be placed after rotation:**

To rotate a point (x, y) 90 degrees clockwise, the mapping is:
\[
(x, y) \to (y, -x)
\]

- For P(−4, 0):
\[
P' = (0, -(-4)) = (0, 4)
\]
- For R(4, -4):
\[
R' = (-4, -4)
\]

Hence, the correct response is: **P′(0, 4) and R′(−4, −4)**.

3. **Determine the degree of rotation and direction for point P(−4,10) and P′(−10,−4):**

Using the rotation mapping for each quadrant:
- A 90-degree clockwise rotation gives (y, -x).
- A 180-degree rotation gives (-x, -y).
- A 270-degree counterclockwise rotation gives (-y, x).

The change from P(−4, 10) to P′(−10, −4):
- The x-coordinate changes from -4 to -10 (which is a shifting down).
- The y-coordinate changes from 10 to -4 (which indicates a shift down).

You can verify that this corresponds to a 270-degree counterclockwise or a -90-degree clockwise rotation. The correct answer is: **−180 degrees (clockwise) or 180 degrees (counterclockwise)** (as a rotation of 180 degrees takes both coordinates to their opposites).

4. **Which of the following mappings is used for a 270-degree (counterclockwise) rotation?**

The mapping for a 270-degree counterclockwise rotation is:
\[
(x, y) \to (-y, x)
\]

So, the correct response is: **(x,y)→(−y,x)**.

### Summary of Answers:
1. a 270 degrees counterclockwise rotation
2. P′(0, 4) and R′(−4, −4)
3. −180 degrees (clockwise) or 180 degrees (counterclockwise)
4. (x,y)→(−y,x)