Question

The orthocentre of the ttiangle abc is b and the circumcentre is s(a,b) if a is the origin then the coordinates of c are

Answer 1

Answer:

Step-by-step explanation:

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 .

The circumcenter of the triangle is .

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 . Lets say the coordinates of 'C' is .

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

Here,  and

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

since (a,b) are the coordinates of the mid-point.

Comparing both the sides, we get:

Therefore, the required coordinates of point C is