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?

A 270° counterclockwise rotation leads to this transformation:

(x,y) → (y, - x)

So, we have

original point        new point

J (-6,2)           →     J' (2,6)

K (-4,6)          →     K' (6,4)

L (-3,3)          →      L' (3,3)

M (-5,-1)        →      M' (-1,5)

So, you have the points J', K', L', and M' that define the new parallelogram.

The coordinates of the endpoints of the side congruent to side KL are the coordinates of K' and L' which are (6,4) and (3,3).