How to calculate the distance between 2 points having coordinates?/ Finding distance by using the distance formula. ~ PARAM VISIONS

The formula for distance (d )between the two points is

d = [ √ ( x2 -x1)² + (y2 - y1)²]

Where, (x1, y1) & (x2, y2) are the coordinates of those two points.

Note: This formula is to calculate the straight line distance in a 2D plane.

Now, let us understand this with derivation & an example.

Let us assume the distance between the two points A & B as d.

In a right-angle triangle ABC,

AB² = [BC² + AC²]

(By Pythagoras theorem)

Here,

Side AB = d

Side AC = (y2 -y1)

Side BC = ( x2 -x1)

Therefore,

d² = [(x2 -x1)² + (y2 - y1)²]

d = [√ ( x2 -x1)² + (y2 - y1)²]

Eg:

Find the distance between the two points A & B, having coordinates (12, 10) & (-7, -5) respectively.

Distance between AB

d = [√ {x2 -x1}² + {y2 - y1}²]

= [√ {12- ( -7)}² + {10 - ( -5)}²]

= [√ {19}² + {15}²]

= [√ {361 + 225}]

= [√ 586]

d = 24.207 units.

Note:

1. If the values of x1 & x2 or y1 & y2 are interchanged, the answer will be the same.

2. Whatever the unit of coordinates, the derived distance shall be denoted in the same unit.

To go through the articles on Estimation & calculation in civil engineering, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

PARAM VISIONS