Answer
$$\left(8,\:-6\right)$$
Work Step by Step
Using the distance formula, we find:
$$\sqrt{\left(10-6\right)^2+\left(-9-\left(-3\right)\right)^2}\\ 2\sqrt{13}$$
Using the midpoint formula, we find:
$$\left(\frac{10+6}{2},\:\frac{-9-3}{2}\right)\\ \left(8,\:-6\right)$$