The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

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Solution

Midpoint of AC = $left parenthesis fraction numerator 2 plus 11 over denominator 2 end fraction comma fraction numerator 0 plus 6 over denominator 2 end fraction right parenthesis equals left parenthesis 13 over 2 comma 3 right parenthesis$
Midpoint of BD = $left parenthesis fraction numerator 9 plus 4 over denominator 2 end fraction comma fraction numerator 1 plus 4 over denominator 2 end fraction right parenthesis equals left parenthesis 13 over 2 comma 5 over 2 right parenthesis$

Midpoint of AC is not equal to midpoint of BD.

Hence diagonals do not bisect each other. Hence it is not a rhombus.

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