To get from your house to your grandparent’s house you must avoid walking through a pond......To avoid the pond, you walk 0.5 miles south and 1.2...

To reach your grandparent’s house from your house while
having to avoid walking through a pond you have to walk 0.5 miles south and 1.2 miles
east.

If it were possible to walk through the pond the
distance you would have to travel would be given by sqrt (0.5^2 + 1.2^2). This follows
from the fact that when you walk towards the south and the east you are walking in
perpendicular directions. We can consider them to be the legs of a right triangle and
use the Pythagorean Theorem to find the length of the
hypotenuse.

sqrt (0.5^2 +
1.2^2)

=> sqrt (0.25 +
1.44)

=> sqrt
(1.69)

=> 1.3

The total
distance you would travel here is 1.3 m. The distance you avoid walking
is:

0.5 + 1.2 - 1.3 = 1.7 - 1.3 =
0.4

The distance you would avoid walking  is
given by option A or 0.4 miles.