Question

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

Answer 1

To rotate a point 90° clockwise about the origin, we can use the rotation matrix:

[cos(θ) -sin(θ)]
[sin(θ) cos(θ)]

For a 90° clockwise rotation, θ is equal to -π/2:

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

Simplifying the matrix, we have:

[0 -(-1)]
[1 0 ]

Evaluating the matrix multiplication gives us the coordinates of C':

C' = [0 -(-3)] [1 1]
[1 1 ] [1 1]
[-3 0]
[2 2]

Therefore, the coordinates of C' are (0, -3).