Page 45 - Mathematics Class - X

ACTIVITY 3.2

OBJECTIVE

To verify section formula by graphical method.

MATERIALS REQUIRED

Cardboard Graph paper Geometry box
Chart paper Glue Pen/pencil

PRE-REQUISITE KNOWLEDGE

1. Concept of Cartesian coordinates 2. Concept of finding distance between two points

THEORY
Section formula: The coordinates of a point P(x, y) which divides the line segment joining A (x , y ) and
1 1
 mx + m x m y + m y 
B (x , y ) internally in the ratio m : m are 1 2 2 1 , 1 2 2 1 .
2 2 1 2  m + m m + m 
 1 2 1 2 
PROCEDURE

1. Paste a chart paper on a cardboard of convenient size.
2. Paste a graph paper on the chart paper.

3. Draw the axes X′OX and YOY ′ on the graph paper as shown in Fig. (a).
4. Take two points A(x , y ) and B(x , y ) on the graph paper as shown in Fig. (b).
1 1 2 2
5. Join A to B to get the line segment AB.

Y Y B (x , y )
6 8 2 2
5 7
4 6
3 5 C
2 4
A (x , y )
1 3 1 1
X' 0 X 2
–5 –4 –3 –2 –1 1 2 3 4 5 6 7
–1 1
–2 X' 0 X
Y' –3 –2 –1 Y' 1 2 3 4 5 6 7
Fig. (a) Fig. (b)

6. Divide the line segment AB internally (in the ratio m : n) at the point C (Fig. (b)).
7. Read the coordinates of the point C from the graph paper.

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