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′(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)
(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)
Answers
Answered by
GPT-4o mini
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)**
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)**
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