Question

# To find: the distance between the lakes to the nearest mile. Given: (26,15) and (9,20)

Alternate coordinate systems
To find: the distance between the lakes to the nearest mile.
Given:
(26,15) and (9,20)

2021-01-24

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