If $\mathrm{A}(3, -4), \mathrm{B}(7, 2)$ are the ends of a diameter of a circle and $\mathrm{C}(3, 2)$ is a point on the circle, then the orthocentre of the $∆\mathrm{ABC}$ is

Given  end points of diameter are $\mathrm{A}=(3, -4), \mathrm{B}=(7, 2)$ 

and C=(3,2) be any point on circle

We know that angle in semi circle is right angle

So, $\overline{\mathrm{BC}}$ is perpendicular to $\overline{\mathrm{AC}}$

$\therefore {∆}^{\mathrm{le}} \mathrm{ABC}$  Is right angle at C

$\therefore$ Orthocenter $\left(\mathrm{C}\right)=(3, 2)$