Question

Imagine a 90° (counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′ . (1 point) Responses (8,4) left parenthesis 8 comma 4 right parenthesis (−8,4) left parenthesis negative 8 comma 4 right parenthesis (8,−4) left parenthesis 8 comma negative 4 right parenthesis (4,−8)

Answer 1

The original coordinate of D is, (-8,-4)

Answer 2

The original coordinate is (-4,-8)

Answer 3

To find the coordinates of point \( D' \) after a 90° counterclockwise rotation about the origin, you can use the transformation rule for rotation:

If a point has coordinates \( (x, y) \), then after a 90° counterclockwise rotation, the new coordinates \( (x', y') \) will be given by:
\[
(x', y') = (-y, x)
\]

Assuming point \( D \) has coordinates \( (x, y) \), you would apply the transformation as follows:

1. Flip the sign of the y-coordinate.
2. Move the y-coordinate to the x-coordinate.

If you don't have the original coordinates for point \( D \), it cannot be determined exactly. However, with the provided response options, we can verify if any of them could fit a typical \( (x, y) \) transformation:

- If \( D \) were \( (4, 8) \), then:
\[
D' = (-8, 4)
\]
- If \( D \) were \( (-4, 8) \), then:
\[
D' = (-8, -4)
\]
- If \( D \) were \( (8, 4) \), then:
\[
D' = (-4, 8)
\]

From the given options, the only point that could be derived is **(−8, 4)**.

So, without the specific original coordinates, but based on the provided options, **the correct answer is \( (−8, 4) \)**.

Answer 4

Given that the original coordinate of \( D \) is \( (-8, -4) \), we can apply the 90° counterclockwise rotation transformation:

Using the rotation formula:
\[
(x', y') = (-y, x)
\]

Substituting in the coordinates of point \( D \):

- Original coordinates of \( D \): \( (-8, -4) \)

Now, apply the formula:
\[
x' = -(-4) = 4
\]
\[
y' = -8
\]

Thus, the new coordinates \( D' \) after the rotation will be:
\[
D' = (4, -8)
\]

Therefore, the coordinate of \( D' \) is \( (4, -8) \).

Answer 5

Thank you for the clarification! Given the original coordinates of \( D \) are \( (-4, -8) \), let's apply the 90° counterclockwise rotation about the origin:

Using the rotation formula:

\[
(x', y') = (-y, x)
\]

For the point \( D \) with coordinates \( (-4, -8) \):

1. Calculate \( x' \):
\[
x' = -(-8) = 8
\]

2. Calculate \( y' \):
\[
y' = -4
\]

Therefore, after a 90° counterclockwise rotation, the new coordinates \( D' \) will be:

\[
D' = (8, -4)
\]

So the coordinate of \( D' \) is \( (8, -4) \).