A quadrilateral is drawn on a coordinate plane with vertices G(10,−3) , H(2,6) , J(−4,0) , and K(0,−5) . Use rotation mapping to determine the location of J after a −270 -degree (clockwise) rotation about the origin.(1 point)

Answer 1

To perform a −270-degree clockwise rotation about the origin, we can use the following mapping rule:

(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)

For a −270-degree rotation, θ = −270 degrees.

Now, let's apply the mapping rule to point J(-4, 0):

(x', y') = (-4*cos(-270) - 0*sin(-270), -4*sin(-270) + 0*cos(-270))

To simplify the calculation, we need to convert −270 degrees to radians:

θ(rad) = θ(degrees) * π/180
θ(rad) = -270 * π/180
θ(rad) = -3π/2

(x', y') = (-4*cos(-3π/2) - 0*sin(-3π/2), -4*sin(-3π/2) + 0*cos(-3π/2))

Using the trigonometric identities cos(-θ) = cos(θ) and sin(-θ) = -sin(θ), we get:

(x', y') = (-4*cos(3π/2), -4*(-sin(3π/2)))
(x', y') = (0, 4)

Therefore, after a −270-degree rotation about the origin, the location of J will be (0, 4).