To find the image of point C after a 180-degree counterclockwise rotation about point P, you first identify the coordinates of both points. Then, you reflect point C across point P, effectively moving it to the opposite side of P at an equal distance. The resulting image will be directly opposite C in relation to P, forming a straight line through P.
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).
To rotate an image 180 degrees clockwise, you can use image editing software or programming libraries. In most software, you can usually find a "Rotate" option in the menu, where you can select "180 degrees" or "flip upside down." If using programming libraries like Python's PIL, you can use the rotate(180) function. This process effectively turns the image upside down, achieving the desired rotation.
Fomula(work with both clockwise/counterclockwise):(-x,-y)
To find the image of the point (1, -6) after a 180-degree counterclockwise rotation about the origin, you can use the rotation transformation. A 180-degree rotation changes the coordinates (x, y) to (-x, -y). Therefore, the image of the point (1, -6) is (-1, 6).
The answer will depend on where the centre of rotation is. Since that it not specified, the image could by anywhere.
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
our point A(x,y) becomes A'(-x,-y).
It is (-1, 6).Also, if the rotation is 180 degrees, then clockwise or anticlockwise are irrelevant.It is (-1, 6).
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).
Because 180 degrees clockwise is the same as 180 degrees counterclockwise.
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
What is the image of point (3, 5) if the rotation is
A measure of rotation MUST state whether it is clockwise or anti-clockwise. Unless the rotation is 0 degrees (ie no rotation) or 180 degrees (the two are the same). It must also specify the centre of rotation. Since you have not bothered to share these crucial bits of information, I cannot provide a more useful answer.
Fomula(work with both clockwise/counterclockwise):(-x,-y)
The answer will depend on where the centre of rotation is. Since that it not specified, the image could by anywhere.
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).