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MathsShare > Blog > Posts > Mirror a point in a line - Oxford Mathematics entrance question
Mirror a point in a line - Oxford Mathematics entrance question

The normal to the line ax + by = c is the vector (a,b).
Hence the normal to the line 3x + 4y = 50 is (3,4).

Any point from (x1,y1) on a normal is of the form (x1,y1) + k(a,b) – which is, if I remember rightly, (3,4) + k(3,4) in the example question.  I think only (9,12) on the list of possible answers will fit? (with k=2).

See also http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html

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