In the following figure, the distance from one location to the next is 80 feet. What is the distance directly from Home to school? Is it the same distance as from Shop to Park?

I can't see your diagram, but I assume it is a triangle, with two sides of 80 and the longest side being from the home to the school. Set it up like this:

80^2 + 80^2 = c^2 where the ^ symbol means an exponent

1600 + 1600 = c^2

3200 = c^2 now root both sides

The distance is 56.5. No, it is not the same as from the shop to the park.