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.
270 rule represent a 270 rotation to the left which is very easy
The effect of the rotation is the same as that of a 90 degree clockwise rotation. In matrix notation, it is equivalent to [post-]multiplication by the 2x2 matrix: { 0 1 } {-1 0 }
It is (-6, -1).
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.
It is multiplication by the 2x2 matrix 0 1-1 0
Yes, a 270-degree clockwise rotation is the same as a 90-degree counterclockwise rotation. When you rotate an object 270 degrees clockwise, you effectively move it 90 degrees in the opposite direction, which is counterclockwise. Both rotations will result in the same final orientation of the object.
To find the image of the point (1, -6) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The coordinates transform as follows: (x, y) becomes (y, -x). Therefore, the image of (1, -6) is (-6, -1).
A rotation of 270 degrees clockwise is equivalent to a rotation of 90 degrees counterclockwise. In a Cartesian coordinate system, this means that a point originally at (x, y) will move to (y, -x) after the rotation. Essentially, it shifts the point three-quarters of the way around the origin in the clockwise direction.
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
You went 360o in the same direction, so you end up with a circle.
270 rule represent a 270 rotation to the left which is very easy
A counterclockwise rotation of 270 degrees about the origin is equivalent to a clockwise rotation of 90 degrees. To apply this transformation to a point (x, y), you can use the rule: (x, y) transforms to (y, -x). This means that the x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative of the x-coordinate.
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
The effect of the rotation is the same as that of a 90 degree clockwise rotation. In matrix notation, it is equivalent to [post-]multiplication by the 2x2 matrix: { 0 1 } {-1 0 }
A rotation of 270 degrees counterclockwise about vertex A means that you would turn the point or shape around vertex A in a counterclockwise direction by three-quarters of a full circle. This results in a position that is equivalent to a 90-degree clockwise rotation. The new orientation will place points or vertices in a different location relative to vertex A, effectively shifting them to the left if visualized on a standard Cartesian plane.
A rotation of 270 degrees counterclockwise is a transformation that turns a figure around a fixed point by 270 degrees in the counterclockwise direction. This rotation can be visualized as a quarter turn in the counterclockwise direction. It is equivalent to rotating the figure three-fourths of a full revolution counterclockwise.
It is (6, 1).