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Statement-1: If the circumcentre of a tr...

Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation `5x-3y=0`
Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio `1:2`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement-2 not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
Statement-2 : is true being a geometrical result. The coordinates of the cenrtroi are `((2+4)/(2),(3+7)/(2))` i.e,, (3,5). Let `(x_(1),y_(1))` be the coordinates of orthocentre. Then, (3,5) divides the segment joing (0,0) and (x,y) in the ratio `1:2`
` :. 3=(x_(1))/(3) and 5=(y_(1))/(3) rArr x_(1)=9,y_(1)=15`
Clearly, is satisfies the relation `5x-3y=0`
So, statement-1 : is true. Alos, statement-2 is a correct explanation for statement-1
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