Discussion Forum



1)

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?


A) (A) and (R) are true and (R0 is the correct explanation (A)

B) (A) and (R) are true, but (R) is not the correct explanation to (A)

C) (A) is true , (R) is false

D) (A) is false , (R) is true

Answer:

Option C

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