A rectangle $A B C D$ has its side parallel to the line $y=2 x$ and vertices $A, B, D$ are on lines $y=1, x=1$ and $x=-1$ respectively. The coordinate of $C$ can be

Question

A rectangle $A B C D$ has its side parallel to the line $y=2 x$ and vertices $A, B, D$ are on lines $y=1, x=1$ and $x=-1$ respectively. The coordinate of $C$ can be, $(3,8)$, $(-3,8)$, $(-3,-1)$, None of these

MARKS App · Accepted Answer

Hint: Case I line $y=2 x\ldots(1)$ $A D$ parallel to $y=2 x$ $\Rightarrow \mathrm{M}_{\mathrm{AD}}=2 ~\&~ \mathrm{M}_{\mathrm{AB}}=-\frac{1}{2}$ for $a=3$ $A(3,1), B(1,2), C(-3,-6), D(-1,-7)$ $\begin{aligned} & \text { for } a=-3 \ & C(3,3), A(-3,1), B(1,-1), D(-1,5)\end{aligned}$ Case II AD perpendicular to line (1) $\Rightarrow M_{A D}=\frac{1}{2}, M_{A B}=2 \Rightarrow b=3-2 a \Rightarrow d=\frac{a+1}{2}$ for $a=3, C(-3,-2)$ for $a=-3, C(3,7)$ ${ }^*$ In both cases if abscissa of $C: 3$ or -3 then co-ordinates of $C$ can be $(3,3)$ or $(3,7)$ or $(-3,-6)$ or $(-3,-2)$

Search any question & find its solution

Looking for more such questions to practice?