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 }
(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
270 rule represent a 270 rotation to the left which is very easy
It is multiplication by the 2x2 matrix 0 1-1 0
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(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
The rotation rule for a 180-degree counterclockwise rotation involves turning a point around the origin (0, 0) by half a circle. For any point (x, y), the new coordinates after this rotation become (-x, -y). This means that both the x and y coordinates are negated. For example, the point (3, 4) would rotate to (-3, -4).
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
(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.
A 90-degree counterclockwise rotation transforms a point ((x, y)) in the coordinate plane to the new point ((-y, x)). This means that the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate. This rotation effectively moves the point around the origin in a counterclockwise direction by a quarter turn.
270 rule represent a 270 rotation to the left which is very easy
A 90-degree clockwise rotation about a vertex involves moving each point in the shape a quarter turn to the right around that vertex. For a point ((x, y)), the new coordinates after the rotation will be ((y, -x)) when considering rotation around the origin. If rotating around a different vertex, you first translate the shape so that the vertex becomes the origin, apply the rotation, and then translate back.
(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.
A 270-degree counterclockwise rotation around the origin in a Cartesian coordinate system transforms a point ((x, y)) to the new coordinates ((y, -x)). This means the x-coordinate becomes the y-coordinate, and the y-coordinate changes its sign and becomes the new x-coordinate. Essentially, it rotates the point three-quarters of the way around the origin.
plz awnser this
To rotate a figure 180 degrees clockwise, you can achieve this by first reflecting the figure over the y-axis and then reflecting it over the x-axis. This double reflection effectively rotates the figure 180 degrees clockwise around the origin.
To rotate a figure 90 degrees clockwise around the origin on a coordinate grid, you can use the transformation rule: (x, y) becomes (y, -x). For the point (5, 5), applying this rule results in (5, -5). Therefore, after a 90-degree clockwise rotation, the new coordinates of the point are (5, -5).