What is the distance between (–3, –2) and (1, 4)?

Answer 1

First take the difference of the X coordinates. -3 - 1 = -4
Then the difference of the Y coordinates. -2 - 4 = -6
So the horizontal distance is 4 and vertical distance is 6, we just need to determine the hypotenus.
The formula is a^2 + b^2 = c^2
So
4^2 + 6^2 = c^2
16 + 36 = c^2
52 = c^2
take the square root of both sides
c = 7.211

Answer 2

In Euclidean space, the normal way to calculate distances is the square root of the sum of squares. In this case, the displacements are 4 in x and 6 in y:

distance = SQRT(4*4 + 6*6) = SQRT(16+36) = SQRT(52) = 7.2111...

However, depending on the kind of space you are in or on other conditions of your problem, there exist other "metrics" (as the methods of calculating distances are called).

One is called the "taxicab" method. The distance is found by simply adding the axial displacements.
Here: distance = 4 + 6 = 10.
If the grid represents the streets and avenues of a city, then a cab having to go up 4 streets and over 6 avenues will have to cover 10 blocks (the cab cannot cut through the buildings to use the hypothenuses).

Answer 3

Over 4 and up 6

4^2 + 6^2 = 16 + 36 = 52

square root of 52 = [ 7.211 ]