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

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(C) In a parallelogram,the diagonals bisect each other at their midpoint. Let the midpoint of diagonal $PR$ be $M_1$ and the midpoint of diagonal $QS$

Vedclass · Accepted Answer

$a = 2, b = 3$

Vedclass · Answer

(C) In a parallelogram,the diagonals bisect each other at their midpoint. Let the midpoint of diagonal $PR$ be $M_1$ and the midpoint of diagonal $QS$ be $M_2$. Since $M_1 = M_2$,we have: Midpoint of $PR = (\frac{1+5}{2}, \frac{2+7}{2}) = (3, 4.5)$ Midpoint of $QS = (\frac{4+a}{2}, \frac{6+b}{2})$ Equating the coordinates: $\frac{4+a}{2} = 3$ $\Rightarrow 4+a = 6$ $\Rightarrow a = 2$ $\frac{6+b}{2} = 4.5$ $\Rightarrow 6+b = 9$ $\Rightarrow b = 3$ 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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