Question

Let $ABCDEF$ be a regular hexagon. If $AD=xBC$ and $CF=yAB$, then $xy=$

• A. 4
• B. -4
• C. 2
• D. -2

Answer 1

Answer: (B)

Since $ABCDEF$ is a regular hexagon, from plane geometry, we have

$AD=2BC$ and $FC=2AB$
$\therefore AD=2BC$ and $FC=2AB(1)$.
Given that $AD=xBC$.
$\therefore 2BC=xBC$, by (i)
$\Rightarrow x=2(2)$
Again, given that $CF=yAB$
or $-FC=yAB$.
$\therefore -2AB=yAB$, using (ii)
$\Rightarrow y=-2(3)$.
From (ii) and (iii),
$xy=2(-2)=-4$.