If you look the data of the question carefully, you will find it as a right angle triangle.
Then vertices are = (10, 0) , (0, 24) (10, 24)
Hence orthocentre will be at the mid point of its hypotenuse i.e.
[(10+0)/2 , (0+24)/2]
(5, 12)
Regards
Arun (askIITians forum expert)