We know that if we want to reflect any point over an origin, i.e. O ( 0 , 0 ) , we can use matrix transformation like this ( x ′ y ′ ) = ( − 1 0 0 − 1 ) ( x y ) = ( − x − y ) .But, what if we reflect any point over another point M ( a , b ) with a , b ≠ 0

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We know that if we want to reflect any point over an origin, i.e.   O      (    0    ,    0    )  , we can use matrix transformation like this      (                                        x            ′                                                            y            ′                                )    =      (                            −          1                          0                                      0                          −          1                      )        (                            x                                      y                      )    =      (                            −          x                                      −          y                      )    .But, what if we reflect any point over another point   M      (    a    ,    b    )   with   a  ,  b  ≠  0

pomastitxz27r · Accepted Answer

his would not generally be a linear transformation since (0,0) would not map to itself via a reflection over a non-origin point. So you will not be able to do this with a single matrix multiplication.I would suggest translating the coordinate system so that the reflection point is at the new origin; then reflect; and then translate back.For example, to translate (x,y) over (5,7), I would do       (                                        x            ′                                                            y            ′                                )    =      (                            x          −          5                                      y          −          7                      )        (                            −          1                          0                                      0                          −          1                      )    +      (                            5                                      7                      )

We know that if we want to reflect any point over an origin, i.e. O ( 0 , 0

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