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Q: What is the image of the point (-2,7) after a rotation of 180 counterclockwise about the origin?

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The answer will depend on whether the rotation is clockwise or counterclockwise.

What is the image of point (3, 5) if the rotation is

Both will end up on the same place. Using a compass rose as an example: 270 clockwise will point to the west. 90 counterclockwise will also point west.

The image is (-5, 3)

The answer will depend on where the centre of rotation is. Since that it not specified, the image could by anywhere.

The answer depends on the centre of rotation. Since this is not given, there can be no answer.

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).

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The answer depends on the centre of rotation. A rotation cannot be described without specifying the centre of rotation.

A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)

(-5,3)

It is: (-4, -3)

It then is: (-3, -5)

Conventionally positive angles are measured anticlockwise. It depends where the centre of rotation is, so where would you like the image to be? If the centre is at, say, (3, 5) then the image will be at (3, 5) regardless of the angle of rotation. If the centre is at, say, (3, 3) then the image will be at (5, 3) If the centre is at, say, the origin, ie (0, 0) then the image will be at (5, -3).

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).

(x,y)-->(y,-x) A transformation in which every point moves along a circular path around a fixed point

If the point (3,5) is rotated 180 degrees, it becomes (-3,-5).

If the original point was (-4, 12) then the image is (-16, 48).

Point A has coordinates (x,y). Point B (Point A rotated 270°) has coordinates (y,-x). Point C (horizontal image of Point B) has coordinates (-y,-x).

The general direction of rotation of everything in the solar system is anticlockwise (counterclockwise) when viewed from an imaginary distant point above the Earth's North pole.If a planet spins the other way, clockwise, we call that sort of rotation "retrograde".

The coords are (6, 1).

The answer will depend on where the centre of rotation is. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.

Of course. A reflection of any symmetric shape about a line perpendicular to its axis of symmetry will be a rotation of 180 degrees around the point on its axis of symmetry which is halfway between the pre-image and the image.

(-4,-3) anything with a 180 degree rotation regardless of being postive or negative is always negative the numbers in parenthesis.

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