question_answer

If the orthocentre and centroid of a triangle are \[(-3,5)\] and \[(3,3)\] respectively, then the circumcentre is:

A) \[(6,2)\]

B) \[(0,8)\]

C) \[(6,-2)\]

D) \[(0,4)\]

Correct Answer: A

Solution :

[a]

Orthocentre centroid and circumcentre of a triangle are collinear and centroid divides them in the ratio \[2:1\].

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{2x-3}{3}=3\] and \[\frac{2y+5}{3}=3\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=6,\,\,\,y=2\]

Hence, circumcentre is \[(6,2)\].