My neighborhood is full of one-way streets. To drive from my house to the grocery store, I have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. Each block is \(\frac{1}{16}\) of a mile. How much shorter would my trip be if I could fly like a bird (that is, travel in a straight line)?

Explain your solution, and give your answer in miles.

KeyLimePi Mar 17, 2019

#1**+1 **

Let's suppose that your house is located at (0,0)

1 block south from here puts you at (0, -1/16)

1 block east from here now puts you at (1/16, -1/16)

5 blocks north from here puts you at (1/16, 4/16)

2 blocks east from here puts you at (3/16, 4/16)

You have traveled (1/16) ( 1 + 1 + 5 + 2) = 9 / 16 of a mile

The "straightline" distance between (0, 0) and (3/16, 4/16) =

sqrt [ (3/16^2 + (4/16)^2 ] = sqrt [ 25 / 256] = 5 /16 of a mile

So....your trip would be [ 9/16 - 5/16 ] = 4/16 = 1/4 of a mile shorter

CPhill Mar 17, 2019

#2**+4 **

First, I advise you to draw this on a coordinate plane. The bird travels 9 blocks, for a total of 9*1/16=9/16 miles.

Starting Point: (0,0).

Next Point: (0, -1)

Next Point: (1, -1)

Next Point: (1, 4)

Final Point: (3, 4)

Use the distance formula from (0,0) to (3,4) to get a result of 5, so 5*1/16=5/16 miles.

Thus, the answer should be 9/16-5/16=4/16=1/4 of a mile shorter.

tertre Mar 17, 2019