Question

The orthocenter of the triangle $ABC$ is $B$ and the circumcenter is $S(a,b)$. If $A$ is the origin, then the co-ordinates of $C$ are -

• A. $(2a,2b)$
• B. $(\frac{a}{2},\frac{b}{2})$
• C. $\left(\sqrt{a^2+b^2,0}\right)$
• D. $None$

Answer 1

The correct option is B $(\frac{a}{2},\frac{b}{2})$

Given that,

Orthocenter $=A(0,0)$

Circumcenter $=S(a,b)$

Coordinates of $C=$ Coordinates of midpoint

$=(\frac{a+0}{2},\frac{b+0}{2})$

$=(\frac{a}{2},\frac{b}{2})$

Hence, this is the answer.