How do you rotate a figure 90 degrees clockwise about origin? - Answers

Switch the coordinates and change the sign of the second one by multiplying it by negative 1. Here are some examples and a more general way to understand the problem. Consider the point (1,1), a 90 degree rotation clockwise about the origin would move it into the 4th quadrant. The new point is (1,-1) , similarly (-4,2)-> (2,4), (-4,3)-> (3,4) We take a point p= (x,y) the the result of rotation p 90 clockwise about the orgin is a new point p'=(x',y')= (-y, x). . In the case of p=(1,0) the new point is p'= (0, -1) One can use a matrix where the first row is cos(a), sin(a) and the second row is -sin(a) cos(a) for any clockwise rotation of a degrees about the origin. If we let a=90 degrees we have [0 1] as the first row and [-1 0] as the second row. So the matrix is: |0 1| |-1 0| Call that matrix M So a point p= (x,y) can be multiplied by M as follows Mp=p' where p' is the rotated point. If p=(-4,2) then Mp is M(-4,2) which after matrix multiplication means x'=0*-4+1*2=2 and y'=-1*-4+0*2=4 So p'=(2,4) Try it with (1,0) x'=1*0+0*1=0 y'=-1*1+0*1=-1 so p'=(0,-1) and (1,0)->(0,-1) How about the point on the y axis (0,1), it should go to the point (1,0) 0*1+1*1=1 and -1*0+0*1 gives you the pont (1,0) ( we don't see the negative sign because -0 is just 0)