Use the image to answer the question.

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)

GPT-4o mini · Answer

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.