I need help on this question

  C)  rotation 180° about the origin

Step-by-step explanation:

Rotation by 90° or 270° will move a figure from one quadrant to an adjacent quadrant. Your figure has moved to the opposite quadrant, so its rotation must be 180°.

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You have probably seen the transformations ...

  (x, y) ⇒ (-y, x) . . . . . rotation 90° CCW or 270° CW

  (x, y) ⇒ (-x, -y) . . . . . rotation 180°

  (x, y) ⇒ (y, -x) . . . . . . rotation 90° CW or 270° CCW

For rotations through other angles, the relation is ...

  (x, y) ⇒ (x·cos(θ)-y·sin(θ), x·sin(θ)+y·cos(θ)) . . . . rotation CCW by angle θ

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If you compare the above transformations to the given pairs of coordinates, you see the coordinates correspond to rotation by 180°. (Both x- and y-values are negated, but not swapped.)

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step-by-step explanation:

hopefully im right

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: