Question

If the orthocenter and centroid of a traingle are (-3,5) and (3,3) then its circumcenter is

• A. (6,2)
• B. (3,-1)
• C. (-3,5)
• D. (-3,1)

Answer 1

The correct option is A (6,2)

Given,

Orhocenter H(-3,5) and Centroid G(3,3)

Let C(h,k) be the circumcenter of triangle

As we know Centroid divides the line segment joining the Circumcenter and orthocenter in ratio 1:2

Coordinates of Centroid=$(\frac{-3+2h}{1+2},\frac{5+2k}{1+2})$

$⟹(3,3)=(\frac{2h-3}{3},\frac{2k+5}{3})$

Equating Both sides we get,

$2h-3=9,2k+5=9⟹h=6,k=2$

Hence Circumcenter of triangle are $(6,2)$