i need to find the orthocenter of a triangle
the cooridinates are:
X = 55, 51
Y= 10 , 4
Z = 49, 95
and if you can, can you show work
Thank You very much for your help
Hello misterriceman
Suppose that the orthocentre, O, has coordinates . Then we use the fact that the line joining the orthocentre to any vertex is perpendicular to the opposite side. So:
Gradient of OX =
Gradient of YZ =
So the product of these gradients is ; i.e.
(1)
In a similar way, using OZ and XY, we get:
(2)
Now solve the simultaneous equations (1) and (2) to find and . (Horrible numbers!) I make this:
and
I think you should check my working!
Grandad