Question

The point Q(- 5, - 9) is rotated -270about the origin. Select the location of Q'

Answer 1

To rotate a point about the origin counterclockwise, we can use the following formula:

(x', y') = (x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta))

In this case, the angle of rotation is -270 degrees. Converting this to radians, we have theta = -270 * pi / 180 = -3pi / 2.

Let's substitute the coordinates of Q(-5, -9) into the formula:

(x', y') = (-5 * cos(-3pi / 2) - (-9) * sin(-3pi / 2), -5 * sin(-3pi / 2) + (-9) * cos(-3pi / 2))

Now, let's calculate:

(x', y') = (-5 * 0 - (-9) * (-1), -5 * (-1) + (-9) * 0)
= (0 + 9, 5 + 0)
= (9, 5)

Therefore, after rotating Q(-5, -9) counterclockwise by -270 degrees about the origin, the new location Q' is (9, 5).