Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex.

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Solution

Diagonals of parallelogram bisect each other, hence the midpoint of AC= midpoint of BD

$left parenthesis fraction numerator negative 2 plus 4 over denominator 2 end fraction comma fraction numerator negative 1 plus 3 over denominator 2 end fraction right parenthesis equals left parenthesis fraction numerator 1 plus x over denominator 2 end fraction comma fraction numerator 0 plus y over denominator 2 end fraction right parenthesis left parenthesis 1 comma 1 right parenthesis equals left parenthesis fraction numerator begin display style 1 plus x end style over denominator begin display style 2 end style end fraction comma fraction numerator begin display style 0 plus y end style over denominator begin display style 2 end style end fraction right parenthesis x plus 1 equals 2 x space equals 1 y equals 2 H e n c e space t h e space f o u r t h space p o i n t space i s space left parenthesis 1 comma 2 right parenthesis$

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