Question

Use the image to answer the question.

Five solid lines join five plotted points labeled upper I, upper F, upper Y, upper H, and upper S on a coordinate plane. An unlabeled point is also plotted on the plane.

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.

(1 point)
Responses

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

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

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

Y′(1,−9)

Answer 1

To find the coordinates of point \( Y' \) after a 270-degree clockwise rotation about the origin, we can use the rotation transformation formulas.

For a point \( (x, y) \):

- A 90-degree clockwise rotation transforms the point to \( (y, -x) \).
- A 180-degree rotation transforms the point to \( (-x, -y) \).
- A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation, which transforms the point to \( (-y, x) \).

If you have the coordinates of \( Y \) (let's denote them as \( (x, y) \)), you would apply the transformation for a 270-degree clockwise rotation.

Assuming the coordinates of point \( Y \) were provided or known (for example, let’s say they are \( (a, b) \)), applying the transformation would give us:

\[
Y' = (-b, a)
\]

Since you didn't provide the initial coordinates of point \( Y \), I cannot calculate the precise new coordinates for \( Y' \). However, please check the list of provided options against your known coordinates for \( Y \) and apply the transformation.

Here's how you can assess the options mentioned:

- If \( Y \) was at \( (x, y) \):
- \( Y'(-9, 1) \) corresponds to \( (-1, 9) \)
- \( Y'(1, 9) \) corresponds to \( (9, 1) \)
- \( Y'(-1, 9) \) corresponds to \( (9, -1) \)
- \( Y'(1, -9) \) corresponds to \( (-9, 1) \)

Cross-reference these calculated options with your original coordinates to determine which one fits the transformation rule applying a 270-degree rotation. If you provide the coordinates of \( Y \), I can help find the exact result.