Three of the vertices of a parallelogram are $$(2, -7)$$, $$(2, 0)$$ and $$(1, 8)$$ if the fourth vertex is

Solution

If three vertices are $$P$$, $$Q$$, $$R$$, the fourth vertex can be $$P + R - Q$$, $$P + Q - R$$ or $$Q + R - P$$, depending on which given vertex is opposite it. These give $$(2, -7) + (1, 8) - (2, 0) = (1, 1)$$, $$(2, -7) + (2, 0) - (1, 8) = (3, -15)$$ and $$(2, 0) + (1, 8) - (2, -7) = (1, 15)$$. Hence options a, b and c are all possible; $$(7, -8)$$ is not.

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