What is the pH of a solution that results from diluting 0.50mol formic acid (HCO2H) and 0.10 mol sodium formate (NaHCO2) with water to a volume of 1.0 L? (Ka of HCO2H = 1.8 x 10^-4)

This comes from the definition of Ka:

K_a\,=\,\frac {[H^+][HCO_2^-]}{[HCO_2H]

where the numbers in brackets, [] are concentrations (moles/liter)

\large 1.8 \cdot 10^{-4}\,=\,\frac {[H^+][HCO_2^-]}{[HCO_2H] (equation 1)

[HCO_2H] \approx 0.50\, \frac {mole}{liter}

[HCO_2] \approx 0.10\, \frac {mole}{liter}

Enter those into equation 1, above, and solve for [H^+]. The pH is defined as:

pH\,=\,-log([H^+]) (equation 2)

so, once you have found the hydrogen ion concentration (equation 1), calculate the pH from equation 2.