Question

Three vertices of a parallelogram are and . Find the coordinates of the fourth vertex.

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Solution
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Given three vertices of a parallelogram are   and .

Let the coordinates of the fourth vertex be .

We know that the diagonals of a parallelogram bisect each other.

Therefore in parallelogram , and bisect each other .

Mid-point of Mid-point of





and

and

Thus, the coordinates of the fourth vertex are

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