Question

Item 6 Your city is represented in a coordinate plane where each unit represents 1 kilometer. The library is at (−3, −3), the post office is at (2, 2), and your house is at (−5, 2). You ride your bike from your house to the library, then the post office, and then back home. What is the minimum distance that you can ride your bike? Round your answer to the nearest tenth. km

Answer 1

We know, shortest distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is :

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

So, distance between house and library is :

$d_1=\sqrt{(-5-(-3))^2+(2-(-3))^2}\\\\d_1=5.39\ km$

Distance between library and post office :

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(-3-2)^2+(-3-2)^2}\\\\D=7.07\ km$

Distance between post office and house :

$D=\sqrt{(2-(-5)^2)+(2-2)^2}\\\\D=7\ km$

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.