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 1 comma 9 right parenthesis

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

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

Y′(−1,9)

Answer 1

To find the coordinates of the point Y after a 270-degree clockwise rotation about the origin, we can use the rules for rotating points in the Cartesian plane.

For a 270-degree clockwise rotation, the transformation can be described as follows:

• If the original coordinates of the point are \((x, y)\), then after a 270-degree clockwise rotation, the new coordinates will be \((y, -x)\).

Let's assume the coordinates of point Y are \((x, y)\).

You would apply the transformation based on the original coordinates:

1. Y'(x, y) → Y''(y, -x)

Now, the options given are:

• Y′(1,9)
• Y′(1,−9)
• Y′(−9,1)
• Y′(−1,9)

We can check the transformations:

1. If \(Y(1, 9)\):

   • After the rotation: \(Y'(9, -1)\) which isn't an option.

2. If \(Y(1, -9)\):

   • After the rotation: \(Y'(-9, -1)\) which isn't an option.

3. If \(Y(-9, 1)\):

   • After the rotation: \(Y'(1, 9)\) which matches the first option.

4. If \(Y(-1, 9)\):

   • After the rotation: \(Y'(9, 1)\) which isn't an option.

Thus, if Y corresponds to \(Y(-9, 1)\), the correct answer after a 270-degree clockwise rotation about the origin is \(Y′(1, 9)\).

Therefore, the answer is:

Y′(1,9)