Questions
If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the line joining the point is and then the orthocentre satisfies the equation
detailed solution
Correct option is D
The circumcentre is at the origin and the centroidis at a2+1+2a2,a2+1−2a2 i.e at (a+1)22,(a−1)22Let (x, y) be the coordinates of the orthocentre. Since centroid divides the line segment joining circumcentre and orthocentre in the ratio 1 : 2. ∴ (a+1)22=x3 and a(a−1)22=y3⇒ (a+1)2(a−1)2=xy⇒(a−1)2x=(a+1)2yTalk to our academic expert!
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If an triangle circumcentre and orthocentre then the coordinates of the midpoint of the side opposite to A are
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