thank you so much for this
To verify your calculations, place the co-ordinates of the orthocentre into the equations of the perpendicular lines.
The orthocentre is a point on both of the perpendiculars, which contain the opposite vertex (actually all 3 perpendiculars).
If you calculate the orthocentre correctly,
which you did except for having the sign on the y co-ordinate wrong,
you should now be able to place x=49.5 into both and
and get the exact same y=-22 approx for both.
Or you could use y and find that you get the same x=49.5 for both
(or all 3 perpendiculars, if you formulate the 3rd one).
When you draw hand sketches, normally the co-ordinates will be a little bit
off, since you'd have to draw extremely accurately.
Solving the equations is very exact, though it's best to write
the x and y co-ordinates of the centres as fractions rather than decimals.
Practice and you'll improve fast.
Circumcentre and orthocentre are good for mastering line equations.