A fish was plotted on a coordinate plane. Identify the coordinates of the image of Y that would create a 270-degree clockwise rotation about the origin.

Question

(1 point)
Responses

Y′(−1,9)
upper Y prime left parenthesis negative 1 comma 9 right parenthesis

Y′(1,−9)
upper Y prime left parenthesis 1 comma negative 9 right parenthesis

Y′(1,9)
upper Y prime left parenthesis 1 comma 9 right parenthesis

Y′(−9,1)

y = (-9,-1)

Answer 1

To find the coordinates of point \( Y \) after a 270-degree clockwise rotation about the origin, we can use the following rule for rotation:

• A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation. The transformation rules are as follows:
  • \( (x, y) \) transforms to \( (y, -x) \).

Given that we don't have the original coordinates of point \( Y \), I'll provide you with a generic solution with respect to the available responses.

Assuming:

1. If \( Y \) originally were at \( (x, y) \):

   • After a 270-degree clockwise rotation or a 90-degree counterclockwise rotation, the new coordinates become:
   • \( Y' = (y, -x) \).

Now, let's analyze the provided options:

1. \( Y'(-1, 9) \)
2. \( Y'(1, -9) \)
3. \( Y'(1, 9) \)
4. \( Y'(-9, 1) \)
5. \( Y = (-9, -1) \)

To match a coordinate transformation from \( (x, y) \) into one of these forms, we would need to know the original coordinates of \( Y \).

However, if we assume that \( Y \) is given as \( (9, 1) \), for example:

• Applying the transformation gives us \( Y' = (1, -9) \) which matches:
  • Response: \( Y'(1, -9) \).

Note: Without the original coordinates of \( Y \), it is impossible to definitively identify the correct transformed coordinates. If you provide the original coordinates of \( Y \), I can give you the precise answer.

Answer 2

the origional coordinates are (-9,-1)

Answer 3

Given the original coordinates of point \( Y \) as \( (-9, -1) \), we will apply the transformation for a 270-degree clockwise rotation about the origin.

Using the rule for rotation:

• A 270-degree clockwise rotation (which is equivalent to a 90-degree counterclockwise rotation) transforms the coordinates as follows:
• \( (x, y) \) transforms to \( (y, -x) \).

Now, substituting the original coordinates into this transformation:

• Let \( Y = (-9, -1) \).
• Apply the transformation:
  • New coordinates \( Y' = (-1, 9) \).

Thus, after the rotation, the coordinates of \( Y' \) are \( (-1, 9) \).

This matches the first response:

• \( Y'(-1, 9) \)

So, the correct answer is: \( Y'(-1, 9) \).