Figure WXYZ has coordinates W (-2, 3), X (0, -2), Y (-6, 0), and Z (-5, 1), and is rotated 90º clockwise about the origin to produce figure W'X'Y'Z'. What are the coordinates for figure W'X'Y'Z'?
For rotation in a plane, about the origin, the transformation equations are
x’ = x.cos(θ) – y.sin(θ)
y’ = x.sin(θ) + y.cos(θ)
where positive (θ) is in the counter-clockwise direction.
For θ = -90°, the equations become,
x’ = 0 – y.(-1)
y’ = x.(-1) + 0
i.e.
x’ = y
y’ = -x
For W(-2,3), (x,y) = (-2,3) -> (x’, y’) = (-y,x) -> W’ = (3, 2)
For X(0, -2), (x,y) = (0, -2) -> (x’, y’) = (-y,x) -> X’ = (-2, 0)
For Y(-6,0), (x,y) = (-6, 0) -> (x’, y’) = (-y,x) -> Y’ = (0, 6)
For Z(-5,1), (x,y) = (-5, 1) -> (x’, y’) = (-y,x) -> Z’ = (1, 5)
The coordinates of the rotated figure now are,
W’ = (3, 2), X’ = (-2, 0), Y’ = (0, 6), Z’ = (1, 5)