Hey... The Distance Formula is derived from the Pythagoras' Theorem... That's not difficult to understand.
Use the graphical method...
Draw any inclined line on a Cartesian Plane.
I have attached a file to this post. Refer to it.
Let A (x, y) and B(x1, y1).
To find the distance between A and B, i.e, the bold black inclined line, you will need to find the length of the two red dotted lines I have named x and y.
Using Pythagoras' Theorem,
Square of longest side = Sum of squares of the two smallest sides.
Send square to the other side...
>>> Longest side= Sq. root of the sum.
And to find the two smallest sides:
x = 3 - 0 [y1 - y]
y = 3 - 0 [x1 - x]
Note that the triangle formed is a right-angled one.
And now substituting the values for x and y, you will come back to the distance formula given.
Actually, this formula is just another way of using the Pythagoras' Theorem. A diagram would help. But it takes time to draw... Maybe by Tuesday, I'll post the diagram here... It would be easy to understand then.
This formula is used both in Maths and Add Maths.
Good Luck!