Question

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

• A. $a=2,b=4$
• B. $a=3,b=4$
• C. $a=2,b=3$
• D. $a=3,b=5$

Answer 1

Answer: (C)

$a=2,b=3$

$P(1,2),Q(4,6),R(5,7)$ and $S(a,b)$

line PQ=>$(y-2)=\frac{4}{3}(x-1)$, slope =$\frac{4}{3}=m_{pq}$

line QR=>$(y-6)=1(x-4)$, slope $=1$=$m_{QR}$

AS $SP\parallel QR$

slope of MP=$m_{QR}=1$=>line $y=x+c_1$ passes through $(1,2)$

=>$c_1=1$

line Sp=$y=x+1$

As $SR\parallel PQ$

slope of SR=$m_{pq}=\frac{4}{3}$,line y=$x\left(\frac{4}{3}\right)+c_2$ pass through $R(5,7)$

$=>c_2=\frac{1}{3}$

line SR=>$3y=4x+1$

=>$x=2=a$

and $y=2+1=3=b$
$S(a,b):S(2,3)=>a=2,b=3$