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.
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.
Yes the 3 interior angles of any triangle always add up to 180 degrees
Rotating a figure 270 degrees is like rotating the figure to the left 90 degrees. I am not sure what formula or rule you use. *Joe Jonas Rocks*
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
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 }
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.
(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 rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .