3 years ago
Suppose a linear transformation: T:R_{2}\rightarrow R_{2} is formed by taking a rotation counterclockwise of 180 degrees, followed by a reflection across the x_{2}-axis. Describe the points that will be moved back to their original position by this transformation.
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Best Answer
gwenstefaniharajukuloverstour Staff answered 3 years ago
gwenstefaniharajukuloverstour Staff answered 3 years ago
Solution: Rotation:
Consider a point (x,y).
Rotate the point by 180 degree counterclockwise such that the point (x,y) to (—x.-y).
Reflection:
Reflect the point (—x,—y) on x_{2} axis that is the vertical axis:
(-x,-y) changes to (x,-y)
Conclusion:
After transformation, (x,y) becomes (x,—y).
Then all the points (x,y) where y= —y or y= 0 satisfy the given transformation.
Therefore, all points (x,y) on the line y=0