Discussion Forum

Assertion (A) if  (-1,3,2) and (5,3,2) are respectively the  orthocentre and circumcentre of a triangle , then (3,3,2) is its centroid.

 Reason  (R)  centroid of the triangle  divides  the line segment joining the orthocentrer and the circumcentre in the ratio 1:2

 Which  one of the following is true?

Answer:

Explanation:

 Except the equilateral  triangle,  the centroid , orthocentre  and circumcentre are collinear and centroid  divides the line segment joining  the orthocentre  and circumcentre in the ratio 2:1. So, if (-1,3,2) and (5,3,2)  are respectively the orthocentre  and circumcentre of triangle  , then coordinate  of centroid is 

$\left(\begin{array}{c}\frac{(-1\times1)+(5\times2)}{1+2},\frac{(3\times1)+(3\times2)}{1+2}\\ \frac{(2\times1)+(2\times2)}{1+2}\end{array}\right)=(3,3,2)$

 So, (A) is true and (R) is false