JEE Advance - Mathematics (1998 - No. 18)
Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.
The statement is false; altitudes of a triangle are never concurrent.
The concurrence point is called the incenter of the triangle.
The concurrence point is called the orthocenter of the triangle.
The proof requires showing that the product of the slopes of perpendicular lines is 1.
The altitudes of a triangle are concurrent only for equilateral triangles.