Answer
Same slope

Work Step by Step
The slope of the secant line is $\frac{b^2-a^2}{b-a} = a+b$
The instantaneous slope at $x=\frac{1}{2}(a+b)$ is $f'(x) = 2x = 2 (\frac{1}{2}(a+b)) = a+b$
Thus, both slopes are equal. The graph below illustrates this as the secant line, in green, is parallel and has the same slope as the tangent line, in purple.