Question

Write the derivation of the distance formula in the coordinate geometry with the help of a diagram.

Answer 1

The derivation of the distance formula in the coordinate geometry with the help of a diagram is as follows:

• Consider the attached final figure while going through the following steps.
• Consider given two arbitrary points A and B in the Cartesian plane  
• First, construct the vertical line segment (line parallel to the y-axis) and a horizontal line segment (line parallel to the x-axis) passing through each of the given points such that they meet at right angle.
• Now, connect the points A and B to get the right-angled triangle.
• Find the legs of the right triangle by subtracting the x-values and the y-values accordingly.
• The distance between the points A and B is just the hypotenuse of the right triangle.
• Finally, applying the concept of the Pythagorean Theorem, the distance formula is calculated as follows:
• hypotenuse = distance = d = √[(x₂ - x₁)² + (y₂ - y₁)²]