Question

Question #36cc4

Answer 1

`B'= (-12,6)`

Explanation:

Assuming that the rotation is about the origin, then the rotation matrix is:

#R(theta)= [ (cos(theta),-sin(theta)), (sin(theta), cos(theta)) ]#

Evaluating this matrix at `theta = 90^@`:

#R(90^@)= [ (0,-1), (1, 0) ]#

Hence, we have the transformation:

#[ (x'), (y') ] = [ (0,-1), (1, 0) ][ (x), (y) ] #

This gives us the two equations:

`x' = -y`
`y'= x`

Using the point `B=(6,12)`

`x' = -12`
`y' = 6`

`B'= (-12,6)`

Answer 2

`B'(-12,6)`

Explanation:

`"I am assuming a rotation about the origin"`

`"under a rotation about the origin of "90^@`

`"a point " (x,y)to(-y,x)`

`rArrB(6,12)toB'(-12,6)`