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′(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) upper Y prime left parenthesis negative 1 comma 9 right parenthesis Y′(1,9)
Answers
Answer
The original coordinates of Y is, (-9,-1)
Answered by
GPT-4o mini
To find the coordinates of point Y after a 270-degree clockwise rotation about the origin, you can use the following transformation rules for rotations.
A 270-degree clockwise rotation (which is equivalent to a 90-degree counterclockwise rotation) can be calculated using this rule:
If the original coordinates of the point Y are (x, y), the new coordinates (x', y') after a 270-degree clockwise rotation will be given by:
- \( x' = y \)
- \( y' = -x \)
To determine the image of point Y after the transformation, we need the original coordinates of point Y.
Since the original point’s coordinates are not given in your question, I’ll assume we rotate point Y from coordinates (x, y). Following the transformation rules:
1. The x-coordinate becomes the y-coordinate: \( x' = y \)
2. The y-coordinate becomes the negative of the x-coordinate: \( y' = -x \)
Given the options:
1. \( Y' (1, -9) \)
2. \( Y' (-9, 1) \)
3. \( Y' (-1, 9) \)
4. \( Y' (1, 9) \)
Based on the transformation, the new coordinates should reflect this change.
Examining the provided responses for potential original coordinates:
1. If we assume Y was (1, -9):
- \( x' = -9 \)
- \( y' = -1 \) → This is not a match.
2. If we assume Y was (-9, 1):
- \( x' = 1 \)
- \( y' = 9 \) → This is not a match.
3. If we assume Y was (-1, 9):
- \( x' = 9 \)
- \( y' = 1 \) → This is not a match.
4. If we assume Y was (1, 9):
- \( x' = 9 \)
- \( y' = -1 \) → This is not a match.
If you are looking for a transformation based on a specific point, please provide the point's coordinates. If not, the Y' coordinates based on the definitions of 270-degree clockwise rotation suggest that given the options, none of the transformations presented match standard point transformations.
To solve this, you would presumably need to know the original point. Assuming one of those coordinates above was the original point, I would conclude based on conventional transformation rules that (1, -9) is the potential answer as it aligns closest to standard transformation rules.
If you have the original coordinates for Y, please share them for a proper analysis!
A 270-degree clockwise rotation (which is equivalent to a 90-degree counterclockwise rotation) can be calculated using this rule:
If the original coordinates of the point Y are (x, y), the new coordinates (x', y') after a 270-degree clockwise rotation will be given by:
- \( x' = y \)
- \( y' = -x \)
To determine the image of point Y after the transformation, we need the original coordinates of point Y.
Since the original point’s coordinates are not given in your question, I’ll assume we rotate point Y from coordinates (x, y). Following the transformation rules:
1. The x-coordinate becomes the y-coordinate: \( x' = y \)
2. The y-coordinate becomes the negative of the x-coordinate: \( y' = -x \)
Given the options:
1. \( Y' (1, -9) \)
2. \( Y' (-9, 1) \)
3. \( Y' (-1, 9) \)
4. \( Y' (1, 9) \)
Based on the transformation, the new coordinates should reflect this change.
Examining the provided responses for potential original coordinates:
1. If we assume Y was (1, -9):
- \( x' = -9 \)
- \( y' = -1 \) → This is not a match.
2. If we assume Y was (-9, 1):
- \( x' = 1 \)
- \( y' = 9 \) → This is not a match.
3. If we assume Y was (-1, 9):
- \( x' = 9 \)
- \( y' = 1 \) → This is not a match.
4. If we assume Y was (1, 9):
- \( x' = 9 \)
- \( y' = -1 \) → This is not a match.
If you are looking for a transformation based on a specific point, please provide the point's coordinates. If not, the Y' coordinates based on the definitions of 270-degree clockwise rotation suggest that given the options, none of the transformations presented match standard point transformations.
To solve this, you would presumably need to know the original point. Assuming one of those coordinates above was the original point, I would conclude based on conventional transformation rules that (1, -9) is the potential answer as it aligns closest to standard transformation rules.
If you have the original coordinates for Y, please share them for a proper analysis!
Answered by
GPT-4o mini
Great! Now that we have the original coordinates of Y as (-9, -1), we can apply the transformation for a 270-degree clockwise rotation about the origin.
Using the transformation rules for a 270-degree clockwise rotation:
For a point \((x, y)\):
- The new x-coordinate (\(x'\)) becomes the y-coordinate:
\[
x' = y
\]
- The new y-coordinate (\(y'\)) becomes the negative x-coordinate:
\[
y' = -x
\]
Substituting \((-9, -1)\) into the formulas:
1. \( x' = y = -1 \)
2. \( y' = -x = -(-9) = 9 \)
So after the rotation, the new coordinates \(Y'\) are:
\[
Y'(-1, 9)
\]
Therefore, the answer is:
### \(Y'(-1, 9)\)
Using the transformation rules for a 270-degree clockwise rotation:
For a point \((x, y)\):
- The new x-coordinate (\(x'\)) becomes the y-coordinate:
\[
x' = y
\]
- The new y-coordinate (\(y'\)) becomes the negative x-coordinate:
\[
y' = -x
\]
Substituting \((-9, -1)\) into the formulas:
1. \( x' = y = -1 \)
2. \( y' = -x = -(-9) = 9 \)
So after the rotation, the new coordinates \(Y'\) are:
\[
Y'(-1, 9)
\]
Therefore, the answer is:
### \(Y'(-1, 9)\)