Question

Find the co - ordinates of the centroid and circumcentre of the triangle whose vertices are (2,3) , (3,4) and (6 , 8) and hence find the co - ordinates of its orthocentre

Answer 1

G is $(\frac{\sum x_1}{3},\frac{\sum y_1}{3})=(\frac{11}{3},5)$ and if O be the circumcentre , then OA = OB = OC and in Q .1 (a) P. 774 - 76 we find that O is $(-\frac{27}{2},\frac{39}{2})$ . If H (h,k) be orthocentre then G divides OH in the ratio 1 : 2
$\therefore$ H is (38 , - 24)