Question

The blocks in a city are all perfect squares. A friend gives you the following directions to a good restaurant; "go north 3 blocks, turn east and go 5 blocks, turn south and go 7 blocks, turn west and go 3 blocks." How far away (straight line distance) is the restaurant?

Answer: _____ blocks

Answer 1

A picture helps.

North means positive in the y direction, South is negative in the y direction, East is positive in the x direction and West is negative in the x direction.

So total x is 5-3=2 and total y is 3-7=-4.

So from the starting point S(0,0) we end up at (2,-4).

The straight line difference uses Pythagoras’ Theorem:

√(2²+(-4)²)=√(4+16)=√20=√(4×5)=2√5=4.4721 blocks approx.

Note that it’s 4+2=6 if you follow the dotted path (south 4 blocks and east 2 blocks), which is not the straight line distance shown by the solid red line.