We know, shortest distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is :
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So, distance between house and library is :
[tex]d_1=\sqrt{(-5-(-3))^2+(2-(-3))^2}\\\\d_1=5.39\ km[/tex]
Distance between library and post office :
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(-3-2)^2+(-3-2)^2}\\\\D=7.07\ km[/tex]
Distance between post office and house :
[tex]D=\sqrt{(2-(-5)^2)+(2-2)^2}\\\\D=7\ km[/tex]
Therefore, minimum distance that you can ride your bike is (5.39+7.07+7) km = 19.46 km.
Hence, this is the required solution.
