See diagram. By definition of the Orthocentre to prove that is theOriginally Posted by thduong711
orthocentre of triangle it is sufficient to prove that extended
is a normal to , and that extended is a normal to .
Now it is sufficient to prove that in general extended is a normal ,
as by an equivalent argument will be a normal to .
Now the best way to proceed as far as I can see is to introduce
coordinates, and use coordinate geometry to show that angle
in the diagram is a right angle.
<<You will need to check the algebra in this carefully>>
Let be the origin , be and be .
Then is .
The slope of is , so the slope of is , in fact
is the line . The line has equation ,
so is the point of intersection of:
Which is the point .
Now lies on , and may be written as for some
To finish find the equation on the line through and , and from that
find the coordinates of . Find the slope of the line through and ,
which should be minus the slope of the line through and .