Math CentralQuandaries & Queries


Question from hanbal, a student:

Could please help solving this problem

A(1,3) and D(5,5) are two vertices of a rectangle ABCD. The equation of line AC is 3y=4x + 5
a) the equation of line DC


What a strange problem. I wonder if you have written it down correctly. THE EQUATION OF AC IS IRRELEVANT! You just have to find the slope of AD, which is the line joining A to D. The slope of the line DC (that you seek) is then the negative of the reciprocal of the slope of AD. (This means that if you found the slope of AD to be p/q, then the slope of DC is -q/p.) The desired line DC has an equation with slope -q/p that is satisfied by (x, y) = (5, 5).


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