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.

Question

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 rule for rotating points in the coordinate plane:

• A 90-degree clockwise rotation transforms a point \((x, y)\) to \((y, -x)\).
• A 180-degree rotation transforms a point \((x, y)\) to \((-x, -y)\).
• A 270-degree clockwise rotation transforms a point \((x, y)\) to \((-y, x)\).

Thus, to determine \(Y'\) from a given point \(Y(x, y)\):

1. Identify the coordinates of \(Y\).
2. Apply the rotation transformation for 270 degrees clockwise: \(Y' = (-y, x)\).

Unfortunately, the coordinates of point \(Y\) are not specified in your problem. If the coordinates of \(Y\) are provided, you can apply the transformation to find \(Y'\).

For example, if \(Y(1, 9)\):

• After a 270-degree clockwise rotation:
  • \(Y' = (-9, 1)\).

So the answer, if \(Y\) is at (1, 9), would be \(Y'(-9, 1)\).

If you have the specific coordinates of point \(Y\), you can calculate accordingly!