What is the image of point (3, 5) if the rotation is
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).
The image is (-5, 3)
It then is: (-3, -5)
The answer depends on the centre of rotation. A rotation cannot be described without specifying the centre of rotation.
What is the image of point (3, 5) if the rotation is
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).
The answer will depend on where the centre of rotation is. Since that it not specified, the image could by anywhere.
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
Conventionally positive angles are measured anticlockwise, by 180° is a half turn regardless of direction. It depends where the centre of rotation is, so where would you like the image to be? If the centre is at, say, (4, 3) then the image will be at (4, 3) regardless of the angle of rotation. If the centre is at, say, (4, 4) then the image will be at (4, 5) If the centre is at, say, the origin, ie (0, 0) then the image will be at (-4, -3).
The image is (-5, 3)
It is: (-4, -3)
It then is: (-3, -5)
It is: (-4, -3)
All rotations, other than those of 180 degrees should be further qualified as being clockwise or counter-clockwise. This one is not and I am assuming that the direction of rotation is the same as measurement of polar angles. Also, a rotation is not properly defined unless the centre of rotation is specified. I am assuming that the centre of rotation is the origin. Without these two assumptions any point in the plane can be the image. With the assumptions, for which there is no valid reason, the image is (3, -4).
(-5,3)