The point C (-3,1) is rotated 90 degree clockwise about the origin . What are the coordinates of C

Answer 1

To rotate a point 90 degrees clockwise about the origin, we can use the following transformation matrix:

[ cos(θ) sin(θ) ]
[ -sin(θ) cos(θ) ]

For a 90-degree clockwise rotation, θ = -π/2. Evaluating the matrix at θ = -π/2, we have:

[ cos(-π/2) sin(-π/2) ]
[ -sin(-π/2) cos(-π/2) ]

Simplifying the matrix, we get:

[ 0 -1 ]
[ 1 0 ]

Now, let's apply this transformation matrix to the point C(-3,1):

[ 0 -1 ] [ -3 ] [ -1 ]
[ 1 0 ] * [ 1 ] = [ -3 ]

Thus, after rotating 90 degrees clockwise about the origin, the coordinates of C become (-1, -3).