Question

orthocentere of triangle with vertices (3^(1/2),10^(1/2), (7^(1/2),6^(1/2),(5^(1/2),8^(1/2)

Answer 1

Find slope of BC. Slope of AD will be the negative reciprocal of slope of BC.
Knowing the slope of AD and that it passes through A, you can find the equation of line AD. Similarly, find the equation of line BE. Find the intersection of AD and BE and that will be the orthocenter.

Answer 2

\(A:(\sqrt{3},\sqrt{10}),~~ B:(\sqrt{7},\sqrt{6}), ~~C:(\sqrt{5},\sqrt{8})\)