Question

If P( 4, 1 ), Q( 8, 2 ), R( 9, 4 ) and S( p, 3 ) are the vertices of a parallelogram, taken in order, then the value of p is : *
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Answer 1

Hope this helps you

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Answer 2

Let P(4,1),Q(8,2)R(9,4) and S(P,3)

We know that the diagonals of a parallelogram bisect each other. So,the midpoint of PR is same as the mid point of QS.

$\sf Mid~ point~ of~ two~ points ~(x_1,y_1)and~(x_2,y_2)~ is~ calculated~ by~ the ~formula\\ \\ \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\\ \\ \implies \dfrac {4+9}{2} ,\dfrac{1+4}{2} = \dfrac{8+p}{2} , \dfrac{2+3}{2} \\ \\ \implies \dfrac {4+9}{2}= \dfrac {8+p}{2} \\ \\ \implies 13=8+p \\ \\ \implies p=13-8 \\ \\ \implies p =5$