Question

if the orthocentre of the triangle ABC is 'B' and the circumcentre is 'S' ( a,b). if A is the origin then the co ordinates of C are-?

Answer 1

It is given that the orthocenter of the triangle ABC is 'B'. We know that ONLY in a right angle triangle a vertex can be an orthocenter.

So, triangle ABC is a right triangle, where $\angle B=90^\circ$.

The circumcenter of the triangle is $S(a,b)$.

It is known that the circumcenter of a right angle triangle is at the mid-point of the hypotenuse.

In our case AC is the hypotenuse and 'S' is the mid-point of the side AC.

It has been given to use that $A(0,0)$. Lets say the coordinates of 'C' is $C(x,y)$.

We need to use mid-point formula to find the coordinates.

$(\frac{x_1+x_2}{2} ),(\frac{y_1+y_2}{2} )$

Here, $x_1=0,y_1=0$ and $x_2=x,y_2=y$

So, using the mid-point formula and equating both the sides we get:

$(\frac{0+x}{2} , \frac{0+y}{2} )=(a,b)$ since (a,b) are the coordinates of the mid-point.

Comparing both the sides, we get:

$\frac{x}{2} =a, \frac{y}{2} =b$

$x=2a, y=2b$

Therefore, the required coordinates of point C is $(2a,2b)$

Answer 2

Answer:

See attachment for answer

Step-by-step explanation:

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