The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage?

Question

anonymous · Answer

Im not sure what branch of maths your working with but i would be inclined to use the fact that multiplying a complex coordinate by i gives a 90degree anticlockwise rotation.
so make (-4,7) -4+7i and work with that ?

anonymous · Answer

$$x=x'\cos(\theta)+y'\sin(\theta)$$$$y=-x'\sin(\theta)+y'\cos(\theta)$$Where$$x'=-4|y'=7|\theta=-90$$

anonymous · Answer

that is a much better way of doing things

anonymous · Answer

@Taplin44, I do not know these equations by heart, I derive them from the same approach you have declared, multiplication of complex numbers

anonymous · Answer

Good to know, Your equations are much more applicable to someone who doesnt know the topic if that is the case though.

amistre64 · Answer

one way to assess it is to draw out a general setup

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