how to find the centroid, circumcenter and orthocenter of a triangle?

If ( m , n ) ; ( u , v ) and ( p , q ) are the vertices of a triangle then
( (m+u+p) /3 , (n+v+q) /3 ) is the centroid ; if ( k , s ) is the circumcenter
then k and s can be found by solving ,
(n - v) / ( u - m ) = ( 2k - m - u ) / ( 2s - v - n ) ..... ( i )
( v - q ) / ( p - u ) = ( 2k - p - u ) / ( 2s - v - q ) ..... ( ii )
if ( w , f ) is the orthocenter then w and f can be found by solving ,
( f - n ) / ( w - m ) = ( u - p ) / ( q - v ) ..... ( 1 )
( f - v ) / ( w - u ) = ( m - p ) / ( q - n ) ..... ( 2 )

"Solution:Given x(73,33)=(x1,y1)
y(33,35)=(x2,y2)
z(52,27)=(x3,y3)
there for centroid of the triangle =[(x1+x2+x3)/3,(y1+y2+y3)/3]
=[(73+33+52)/3,(33+35+27)/3]
=(52.666,31.666)
to find the circumcenter of the triangle
step 1. first we have to find mid point of the triangle
mid point of xy=[(x1+x2)/2,(y1+y2)/2]
xy=(53,34)
yz=(42.5,31)
zx=(62.5,30)
step 2. then find slop of xy (m)=(y2-y1)/(x2-x1)
step 3. again find the slope of the perpendicular bisector = -1/slope of the line.
Step 4.the circucenter equation =y-y1=m(x=x1)
to find the orthocenter of a triangle
step 1. find the slope of the side (m)=y2-y1/x2-x1
step 2. find slope of the altitude =-1/slope of the opposite side in triangle
step 3. find orthocenter of triangle =y-y1=m(x-x1) "