Class 10 Maths Lab Activity: To verify the distance formula by graphical method

OBJECTIVE:

To verify the distance formula by graphical method.

MATERIAL REQUIRED:

Cardboard, chart paper, graph paper, glue, pen/pencil and ruler.

METHOD OF CONSTRUCTION

1. Paste a chart paper on a cardboard of a convenient size.

2. Paste the graph paper on the chart paper.

3. Draw the axes X'OX and Y'OY on the graph paper.

4. Take two points A(a, b) and B(c,d) on the graph paper and join them to get a line segment AB [see Figure].

DEMONSTRATION

1. Calculate the distance AB using distance formula.

2. Measure the distance between the two points A and B using a ruler.

3. The distance calculated by distance formula and distance measured by the ruler are the same.

OBSERVATION

1. Coordinates of the point A are __(2,4)__.

Coordinates of the point B are ___(-6, -2)____.

2. Distance AB, using distance formula is __10 units_.

          ___________________ 
    AB = √(x₂ - x₁)² + (y₂ - y₁)²   
            _________________
         = √(-6-2)² + (-2-4)² 

          ______________      
    AB = √(-8)² + (-6)²       

             ________       ________
          = √ 64 + 36   =  √ 100

    AB = 10 units

3. Actual distance AB measured by ruler is __10 units___.

4. The distance calculated in (2) and actual distance measured in (3) are _same_.

APPLICATION

The distance formula is used in proving a number of results in geometry.