The orthocentre of triangle ABC is B and the circumcentre is S (a,b). If A is the origin, then the Co- ordinates of C are : ..............

(2a,2b)

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Solution

The correct option is A
(2a,2b)

It's given that the orthocentre of triangle ABC is B. It means point B should be the intersection of altitudes from point A and C of the triangle and angle ABC= $90^{o}$
Co-ordinates of point A=(0,0) origin

Co-ordinates of circumcentre (a,b)
Circumcentre should be equidistant from vertices A, B and C
For a right angled triangle, the circum centre is the midpoint of hypotenuse
AS=SC
Let the co-ordinates of C be (x,y)
$\frac{x + 10}{2} = a, \frac{y + 10}{2} = b$
x=2a, y=2b
Co-ordinates of C=(2a, 2b)
Option A is correct

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