If the points P = hat{i} + 2 hat{j},Q = 4 hat | vedclass

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(C) Given vertices of the parallelogram $PQRS$ are $P(1, 2)$,$Q(4, 6)$,$R(5, 7)$,and $S(a, b)$.In a parallelogram,the diagonals bisect each other,mean

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$a = 2, b = 3$

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(C) Given vertices of the parallelogram $PQRS$ are $P(1, 2)$,$Q(4, 6)$,$R(5, 7)$,and $S(a, b)$.In a parallelogram,the diagonals bisect each other,meaning they share the same midpoint.Let $A$ be the midpoint of the diagonals $PR$ and $QS$.The midpoint $A$ of diagonal $PR$ is given by:$A = \left( \frac{1 + 5}{2}, \frac{2 + 7}{2} \right) = \left( \frac{6}{2}, \frac{9}{2} \right) = \left( 3, 4.5 \right)$.The midpoint $A$ of diagonal $QS$ is given by:$A = \left( \frac{4 + a}{2}, \frac{6 + b}{2} \right)$.Equating the coordinates of the midpoints:$\frac{4 + a}{2} = 3 \implies 4 + a = 6 \implies a = 2$.$\frac{6 + b}{2} = 4.5 \implies 6 + b = 9 \implies b = 3$.Therefore,the values are $a = 2$ and $b = 3$.

If the points $P = \hat{i} + 2 \hat{j}$,$Q = 4 \hat{i} + 6 \hat{j}$,$R = 5 \hat{i} + 7 \hat{j}$,and $S = a \hat{i} + b \hat{j}$ are the consecutive vertices of a parallelogram $PQRS$,then:

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