If P(1, 2),Q(4, 6),R(5, 7),and S(a, b) are th | vedclass

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(C) In a parallelogram,the diagonals bisect each other at their midpoint.Therefore,the midpoint of diagonal $PR$ is equal to the midpoint of diagonal

Vedclass · Accepted Answer

$a = 2, b = 3$

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(C) In a parallelogram,the diagonals bisect each other at their midpoint.Therefore,the midpoint of diagonal $PR$ is equal to the midpoint of diagonal $QS$.Midpoint of $PR = (\frac{1+5}{2}, \frac{2+7}{2}) = (3, 4.5)$.Midpoint of $QS = (\frac{a+4}{2}, \frac{b+6}{2})$.Equating the coordinates:$\frac{a+4}{2} = 3$ $\Rightarrow a+4 = 6$ $\Rightarrow a = 2$.$\frac{b+6}{2} = 4.5$ $\Rightarrow b+6 = 9$ $\Rightarrow b = 3$.Thus,$a = 2$ and $b = 3$.

If $P(1, 2)$,$Q(4, 6)$,$R(5, 7)$,and $S(a, b)$ are the vertices of a parallelogram $PQRS$,then:

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