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).
A mapping consists of two sets and a rule for assigning to each element in the first set one or more elements in the second set. We say that A is mapped to B and write this as m: A→B.
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.
They intersect at 90 degrees
Using the cosine rule they are 28.96 degrees, 104.47 degrees and 46.57 degrees which all add up to 180 degrees.
It is multiplication by the 2x2 matrix 0 1-1 0
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
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.
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.
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 }
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).
First of all, if the rotation is 180 degrees then there is no difference clockwise and anti-clockwise so the inclusion of clockwise in the question is redundant. In terms of the coordinate plane, the signs of all coordinates are switched: from + to - and from - to +. So (2, 3) becomes (-2, -3), (-2, 3) becomes (2, -3), (2, -3) becomes (-2, 3) and (-2, -3) becomes (2, 3).
(x,y)-> (-y,x)
(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
(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.
It is an anticlockwise rotation through 90 degrees.