Formula used:

The distance between the points are calculated as

\(\displaystyle{d}^{2}={\left({y}_{{2}}-{y}_{{1}}\right)}^{2}+{\left({x}_{{2}}-{x}_{{1}}\right)}^{2}\)

Calculation:

Let the two lakes be at the points F and E respectively.

The coordinates are

\(\displaystyle{F}{\left({26},{15}\right)}{E}{\left({9},{20}\right)}\)

Apply distance formula by keeping the values of two coordinates

\(\displaystyle{d}=\sqrt{{{\left({26}-{9}\right)}^{2}+{\left({15}-{20}\right)}^{2}}}\)

Or, \(\displaystyle{d}=\sqrt{{{\left({17}\right)}^{2}+{\left(-{5}\right)}^{2}}}\)

Or, \(\displaystyle{d}=\sqrt{{{289}+{25}}}\)

Or, \(\displaystyle{d}=\pm\sqrt{{314}}\)

Or, \(\displaystyle{d}=\sqrt{{314}}\) (distance can't be negative so omit the negative root found)

Reduse the solution to decimals

\(\displaystyle{d}={17.7}\) units

2 units on coordinate scale is equivalent to 1 mile in actual measurements.

Thus, for 17.7 units in coordinates systems

The actual distance will be equal to

\(\displaystyle{\left(\frac{1}{{2}}\right)}{17.7}={8.86}\) miles

Conclusion:

Thus, the distance between the lakes to the nearest mile is 8.86 miles