Question

A is the translation expressed by matrix[3_4]. B is the translation expressed by matrix[-2_1]. And P is the point (-1, -2). Thus: (B○A○B○A○B)(P)= ?

Answer 1

`(BcircAcircBcircAcircB)(P)=(72,-32)`
`color(white)("XXXXXXXXXXXXXXXXXXXXXXXX")`(see note below)

Explanation:

I am unfamiliar with this notation but I have assumed that
`[3"_"4]` is equivalent to the scaling matrix: `[(3,0),(0,4)]`

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`BcircP=B(P)=[(-1,-2)]xx[(-2,0),(0,1)]`
`color(white)("XXX")=[((-1)xx(-2)+(-2)xx0,color(white)("xxx")(-1)xx0,(-2)xx1)]`

`color(white)("XXX")=[(2,-2)]`

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Similarly:
`AcircBcircP=A(B(P))=[(2,-2)]xx[(3,0),(0,4)]`

`color(white)("XXX")=[(6,-8)]`

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`BcircAcircBcircP=[(6,-8)]xx[(-2,0),(0,1)]`

`color(white)("XXX")=[(-12,-8)]`

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`AcircBcircAcircBcirP=[(-12,-8)]xx[(3,0),(0,4)]`

`color(white)("XXX")=[(-36,-32)]`

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`BcircAcircBcircAcircBcircP=[(-36,-32)]xx[(-2,0),(0,1)]`

`color(white)("XXX")=[(72,-32)]`