Mathematics Lab Activity-12 Class X

Mathematics Laboratory Activities on Coordinate Geometry for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 07

coordinate geometry

Activity - 12

Objective

To verify the distance formula by graphical method.

Material Required

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

Procedure

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 [see Fig. 1].

Figure 1

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 Fig. 2].

Figure 2

5. Calculate the distance AB using distance formula.

6. Measure the distance between the two points A and B using a ruler.
7. The distance calculated by distance formula and distance measured by the ruler are the same.

Observations & calculations

1. Coordinates of the point A are (a, b) = (2, 4)

2. Coordinates of the point B are (c, d) = (-6, - 2)

3. Distance AB, using distance formula is

$|AB|=\sqrt{(c-a)^{2}+(d-b)^{2}}$
$|AB|=\sqrt{(-6-2)^{2}+(-2-4)^{2}}$
$|AB|=\sqrt{(-8)^{2}+(-6)^{2}}$
$|AB|=\sqrt{64+36}$
$|AB|=\sqrt{100}=10\;units$
4. Actual distance AB measured by ruler is 10 units.
5. The distance calculated in Step (3) and actual distance measured in Step (4) are EQUAL.