Question

The orthocentre of the $△ABC$ is $B$ and the circumcentre is $S(a,b)$. If $A$ is the origin, then the coordinates of $C$ are

• A. $(2a,2b)$
• B. $(\frac{a}{2},\frac{b}{2})$
• C. $(\sqrt{a^2+b^2},0)$
• D. $Noneofthese$

Answer 1

Answer: (A)

$(2a,2b)$

The orthocentre is at B means$\Delta ABC$ is right angled with $AC$ as hypotenuse.

So, the circumcentre will be at the midpoint of $AC.$

Let the coordinates of C be $(x,y).$

$\therefore$ By applying the midpoint formula, the mid point of $AC$ will be $S(a,b)=(\frac{x+0}{2}+\frac{y+0}{2}).$

$\therefore \frac{x}{2}=a⟹x=2a$ and $\frac{y}{2}=b⟹y=2b.$

$\therefore C(x,y)=C(2a,2b)$