It is: (-4, -3)
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).
(-4,-3) anything with a 180 degree rotation regardless of being postive or negative is always negative the numbers in parenthesis.
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)
To find the image of the point (4, 3) after a 90-degree rotation counterclockwise about the origin, you can use the transformation formula for rotation. The new coordinates will be (-y, x), which means the image of the point (4, 3) will be (-3, 4).
To find the image of the point (4, 3) after a -90-degree rotation (which is equivalent to a 90-degree clockwise rotation), you can use the rotation formula: (x', y') = (y, -x). Applying this to the point (4, 3), the new coordinates become (3, -4). Therefore, the image of the point (4, 3) after a -90-degree rotation is (3, -4).
It then is: (-3, -5)
It is: (-4, -3)