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Mid Point

The points 3,...

Question

The points (3,-4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.

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Solution

A (3,-4) C(-6,2) B (-1,-3)
Let the fourth vertex be D (x,y)
The diagonals of a parallelogram bisect each other.
Hence midpoint of AB =midpoint of CD
$left parenthesis fraction numerator 3 minus 6 over denominator 2 end fraction comma fraction numerator negative 4 plus 2 over denominator 2 end fraction right parenthesis space equals space left parenthesis fraction numerator negative 1 plus x over denominator 2 end fraction comma fraction numerator negative 3 plus y over denominator 2 end fraction right parenthesis left parenthesis fraction numerator negative 3 over denominator 2 end fraction comma negative 1 right parenthesis equals left parenthesis fraction numerator x minus 1 over denominator 2 end fraction comma fraction numerator y minus 3 over denominator 2 end fraction right parenthesis x minus 1 equals negative 3 x equals negative 2 y minus 3 equals negative 2 y equals 1$

The fourth vertex is (-2,1)

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