Question

The coordinate point Q (0,-8) is reflected over the y-axis. Identify the x- and y- coordinates of its image, Q'.

The coordinates of Q' is:

(1 point)
Responses

(-8,0)
(-8,0)

(0,-8)
(0,-8)

(8,0)
(8,0)

(0,8)

The point P (4,2) is rotate to become P'(-2,4). Describe the rotation by degree and direction.(1 point)
Responses

90°
rotation
90 degreesrotation

−90°
rotation
negative 90 degreesrotation

−270°
rotation
negative 270 degreesrotation

180°
rotation

The function f(x)=x^2 − 1
is reflected over the y-axis. Choose the equation that correctly identifies g(x)
.(1 point)
Responses

g(x)=x^2 − 2
g(x)=x^2 − 2

g(x)=x^2 − 1
g(x)=x^2 − 1

g(x)=x^2 +1
g(x)=x^2 +1

g(x)=−x^2 + 1
g(x)=−x^2 + 1

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 6:00, what is the degree measure of the angle formed moving CLOCKWISE?

(1 point)
Responses

210 degrees
210 degrees

150 degrees
150 degrees

120 degrees
120 degrees

330 degrees

Answer 1

Let's go through each question step by step.

1. **Reflecting Point Q(0, -8) over the y-axis:**
- When a point is reflected over the y-axis, the x-coordinate changes its sign, while the y-coordinate remains the same.
- For point Q(0, -8), the reflection Q' would still have an x-coordinate of 0 and remain at y = -8.
- Therefore, the coordinates of Q' are **(0, -8)**.

2. **Describing the rotation from P(4, 2) to P'(-2, 4):**
- The change in the coordinates suggests that there is a rotation.
- To rotate the point (4, 2) to (-2, 4) clockwise, it corresponds to a 90-degree clockwise rotation.
- Thus the correct description of the rotation is **90° rotation**.

3. **Reflecting the function f(x) = x² - 1 over the y-axis:**
- When a function is reflected over the y-axis, the x variable becomes negative (i.e., f(-x)).
- For f(x) = x² - 1, reflecting over the y-axis gives us g(x) = (-x)² - 1 = x² - 1.
- Therefore, the equation that correctly identifies g(x) after this reflection is **g(x) = x² - 1**.

4. **Calculating the clockwise angle from 11:00 to 6:00:**
- 11:00 is at 330 degrees (as each hour represents 30 degrees).
- 6:00 is at 180 degrees.
- Moving clockwise from 11:00 to 6:00, you have:
- 330 degrees to 360 degrees (30 degrees)
- 0 degrees to 180 degrees (another 180 degrees)
- Adding those together gives you 30 + 180 = **210 degrees**.

To summarize:
1. (0, -8)
2. 90° rotation
3. g(x) = x² - 1
4. 210 degrees