Final answer:
The image of point N(3,-6) after a 90 degree counterclockwise rotation around the origin is (6, 3).
Step-by-step explanation:
To graph the image of point N(3,-6) after a rotation of 90 degrees counterclockwise around the origin, we can use the formula for rotating a point in the coordinate plane. The formula is (x', y') = (x*cos(theta) - y*sin(theta), x*sin(theta) + y*cos(theta)), where (x, y) is the original point and (x', y') is the rotated point.
Plugging in the values for N(3,-6) and a rotation of 90 degrees counterclockwise (which is equivalent to theta = pi/2), we get (x', y') = (3*cos(pi/2) - (-6)*sin(pi/2), 3*sin(pi/2) + (-6)*cos(pi/2)). Evaluating these trigonometric functions, we find that (x', y') = (6, 3).
Therefore, the image of N(3,-6) after a rotation of 90 degrees counterclockwise around the origin is (6, 3).