Why is the formula sqrt (x1-x2) ^2 + (y1-y2) ^2 used instead of sqrt (x2-x1) ^2+ (y2-y1) ^2 to find distance between 2 points?

Answer 1

I am not sure if I follow your question fully, but it does not matter which point you subtract from which as long as you are consistent with the points (e.g. x2 is with y2 and not x2, y1)

An example:

What is the distance between the two points (2,4) and (5,7)

If we say that 2,4 is X1, Y1 and 5,7 is X2, Y2 then we have

sqrt ((2-5)^2 + (4-7)^2) ---> sqrt (9+9) --> sqrt (18) = 4ish

if we reverse it and call 5,7 X1, Y1 and 2,4 X2,Y2 the answer will remain the same. We are squaring the difference between the numbers so the order does not matter.

If you get confused with this try using 0,0 as a point in your mind. It is a viable point and it will illustrate that which point you call X1,Y1 or which point you call X2,Y2 does not matter.