So, d = √(x

_{2}- x

_{1})

^{2}+ (y

_{2}- y

_{1})

^{2},

Here, d is distance between the two points and (x

_{1}, y

_{1}) and (x

_{2}, y

_{2}) are the two co-ordinate points of ‘x’ and y- axis. To understand that more deeply we take an example:-

We have two points A (5, 3) and B (8, 7), here x

_{1}=5, y

_{1}= 3, x

_{2}= 8 and y

_{2}= 7. Now putting these values in the above formula we get,

So, d = √[(8 - 5)

^{2}+(7 - 3)

^{2}]= √[(3)

^{2}+(4)

^{2}]=√[9 + 16] = √25 = 5,

Here we can clearly see that the distance between the two points ‘A’ and ‘B’ is 5.

Now we take another example,

Let A(x

_{1}, y

_{1}) = (7, -2) and B (x

_{2}, y

_{2}) = (2, 1). On putting the values,

We get, d=√[(7 - 2)

^{2}+ (-2 -1)

^{2}]= √[(5)

^{2}+ (-3)

^{2}]= √[25 + 9] = √34 = 5.83,

Here we can clearly see that the distance between the two points ‘A’ and ‘B’ is 6.

From above examples it is clear that the distance between the two points in the co-ordinate geometry will always be a positive value. This is because on putting the values in the formula, if there is any negative value in the bracket then it will become positive after squaring. Let’s take another example where we have two points A (5, 6) and B (4, 3) and we have to find out the length of a line passing through these points,

Then by the formula, d = √[(4 - 5)

^{2}+ (3 - 6)

^{2}]=√[(-1)

^{2}+ (-3)

^{2}] = √[1 + 9] = √10 = 3.16.