Answer:
Solution : (- 9, - 3)
Explanation:
Approach 1 : Imagine that this point (3, - 9) is rotated 90 degrees clockwise. We know that this point lies in the fourth quadrant, so if it is rotated 90 degrees, you can imagine the x - coordinate will be greater than the y - coordinate, if you take their absolute value(s). Remember that the new coordinates will also lie in the third quadrant. Based on these requirements we have the resulting point (- 9, - 3) or option c.
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Approach 2 : There is another approach to this, a more exact approach.
Rotation of axis, θ : (x, y) --> (X, Y)
X = xcos(θ) + ysin(θ),
Y = - xsin(θ) + ycos(θ)
Here θ = 90 degrees. Substitute and solve for the exact coordinates.
X = 3cos(90) + - 9sin(90) = 3cos(90) - 9sin(90) = 3 * 0 - 9 * 1 = - 9,
Y = - 3sin(90) + - 9cos(90) = - 3sin(90) - 9cos(90) = - 3 * 1 - 9 * 0 = - 3
As you can see our solution is the same, (- 9, - 3), or option c.