Question

What is the new point after rotating the point (3,-5) 180 degrees clockwise?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the new point after rotating (3, -5) 180 degrees clockwise, we can use the following formula:

(x', y') = (-x, -y)

Using this formula, we can substitute the values of x and y from the given point:

(-x, -y) = (-3, 5)

Therefore, the new point after rotating (3, -5) 180 degrees clockwise is (-3, 5).

Answer 2

If a segment has endpoints (0,4) and (3,4), how long will the segment be after it is rotated 270 degrees clockwise?

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the length of the segment after it is rotated 270 degrees clockwise, we can simply calculate the distance between the two endpoints.

The formula to find the distance between two points (x1, y1) and (x2, y2) is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we substitute the values of the endpoints:

d = sqrt((3 - 0)^2 + (4 - 4)^2)
= sqrt(3^2 + 0)
= sqrt(9)
= 3

Therefore, the length of the segment after it is rotated 270 degrees clockwise is 3.

Answer 4

A square with sides 6 units in length is reflected across the x-axis. How long are the sides in the reflected figure?

Answer 5

[AI-generated answer — Bot GPT 3.5]

When a figure is reflected across the x-axis, the y-coordinates of all its points are multiplied by -1. The x-coordinates remain the same.

Since the square has sides of length 6 units, after reflecting across the x-axis, the x-coordinates will remain the same, while the y-coordinates will be multiplied by -1.

Therefore, the length of the sides in the reflected figure will still be 6 units.

Answer 6

A triangle with an area of 25 square units is rotated 180 degrees clockwise. What is the area of the rotated figure?

Answer 7

[AI-generated answer — Bot GPT 3.5]

When a figure is rotated 180 degrees clockwise, the area of the figure remains the same. Therefore, the area of the rotated figure will still be 25 square units.

Answer 8

100% tysm that was the practice

Answer 9

[AI-generated answer — Bot GPT 3.5]

You're welcome! I'm glad I could help. If you have any more questions, feel free to ask. Good luck with your practice!

Answer 10

1. Demonstrating the properties of rotations, if a line segment with endpoints (0,-3) and (0,-7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?

2. Rotate a point on a line at (-4,6) 180 degrees counterclockwise. What is the resulting point?
3. Jack discovers that the orientation of a triangle is counterclockwise. He then reflects the triangle over the y-axis. What is the orientation of the reflected figure?
A. there is not enough information to tell.
B. the reflected figure has a clockwise orientation.
C. the orientation could be clockwise or counterclockwise depending on how you do the reflection.
D. the reflected figure has a counterclockwise orientation.
4. If a triangle with vertices (4,3), (8,3) and (7,5) is translated to the right 4 units and down 2 units, what are the vertices of the translated figure?
5. Which transformation(s) will result in a figure that has the same orientation as the original figure?

Answer 11

[AI-generated answer — Bot GPT 3.5]

1. To find an endpoint of the line segment after rotating 90 degrees clockwise, we can use the formula for rotating a point (x, y) by 90 degrees clockwise: (x', y') = (y, -x).

Using this formula, we can rotate each endpoint of the line segment:
Endpoint (0, -3) becomes ( -3, 0) after rotating 90 degrees clockwise.
Endpoint (0, -7) becomes (-7, 0) after rotating 90 degrees clockwise.

Therefore, an endpoint of the rotated segment is (-3, 0).

2. To rotate a point (-4, 6) 180 degrees counterclockwise, we can use the formula for rotating a point (x, y) by 180 degrees counterclockwise: (x', y') = (-x, -y).

Using this formula, we can rotate the given point:
(-4, 6) becomes (4, -6) after rotating 180 degrees counterclockwise.

Therefore, the resulting point after rotating is (4, -6).

3. When reflecting a figure over the y-axis, the orientation of the figure remains the same. Counterclockwise orientation remains counterclockwise, and clockwise orientation remains clockwise.

Therefore, the orientation of the reflected figure is counterclockwise (D. the reflected figure has a counterclockwise orientation).

4. To translate the triangle with vertices (4,3), (8,3), and (7,5) to the right 4 units and down 2 units, we simply add the corresponding values to the x and y coordinates.

(4,3) translated becomes (4+4, 3-2) = (8, 1)
(8,3) translated becomes (8+4, 3-2) = (12, 1)
(7,5) translated becomes (7+4, 5-2) = (11, 3)

Therefore, the vertices of the translated figure are (8,1), (12,1), and (11,3).

5. The transformation(s) that will result in a figure that has the same orientation as the original figure are:
- Translation
- Reflection over a line that keeps the orientation unchanged
- Multiple rotations around a point that add up to a full turn (360 degrees)