Question

The point p (-1,2) is rotated to become (2,1). Describe the rotation by degree and direction.

Answer 1

To describe the rotation, we need to determine the angle and direction of rotation.

To find the angle, we can use the slope formula:
slope = (change in y-coordinate)/(change in x-coordinate)

Original slope:
m1 = (2 - 1)/(-1 - 2) = 1/3

After rotation, the slope must be the negative reciprocal of the original slope because perpendicular lines have negative reciprocal slopes. So, the new slope would be -3.

To find the angle, we can use the arctan function:
angle = arctan(slope)

Original angle:
θ1 = arctan(1/3) ≈ 18.43 degrees

After rotation, the new angle would be:
θ2 = arctan(-3)

However, since -3 can be in the second or fourth quadrant, we add or subtract 180 degrees to get the actual angle:
θ2 = arctan(-3) + 180 degrees ≈ 153.43 degrees or θ2 = arctan(-3) - 180 degrees ≈ -153.43 degrees

So, the rotation is either approximately 153.43 degrees counterclockwise or -153.43 degrees clockwise.