Parallelogram JKLM is shown on the coordinate plane below:
Parallelogram JKLM with ordered pairs at J negative 6, 2, at K negative 4, 6, at L negative 3, 3, at M negative 5, negative 1.
If parallelogram JKLM is rotated 270° counterclockwise around the origin, what are the coordinates of the endpoints of the side congruent to side KL in the image parallelogram?
K′(−4, −6); L′(3, −3)
K′(6, 4); L′(3, 3)
K′(−6, −4); L′(−3, −3)
K′(−4, 6); L′(−3, −3)
To rotate the points of parallelogram JKLM 270° counterclockwise around the origin, we use the following rotation matrix:
R = [0 -1]
[1 0]
Let's perform the rotation for points K(-4, 6) and L(-3, 3):
For point K:
K' = [-4*0 - 6*1, -4*1 + 6*0] = [6, -4]
For point L:
L' = [-3*0 - 3*1, -3*1 + 3*0] = [-3, -3]
Therefore, the coordinates of the endpoints of the side congruent to side KL in the rotated image parallelogram are K'(-4, 6) and L'(-3, -3). The correct option is K′(−4, 6); L′(−3, −3).