Mathematics Lab Activity-13 Class X | Coordinate Geometry

By CBSE MATHEMATICS May 16, 2024

Mathematics Lab Activity-13 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 - 13

Objective

To verify section formula by graphical method.

Material Required

Cardboard, chart paper, graph paper, glue, geometry box and pen/pencil.

Procedure

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

2. Paste a 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 (x₁, y₁) and B (x₂, y₂) on the graph paper [see Fig. 2].

5. Join A to B to get the line segment AB.

Figure 2

1. Divide the line segment AB internally (in the ratio m:n) at the point C [see Fig. 2].

2. Read the coordinates of the point C from the graph paper.

3. Using section formula, find the coordinates of C.

4. Coordinates of C obtained from Step 2 and Step 3 are the same.

Observations & calculations

1. Coordinates of A are (2, 4).
2. Coordinates of B are (6, 8).
3. Point C divides AB in the ratio 1 : 3.
4. Coordinates of C from the graph paper are (3, 5).
5. Coordinates of C by using section formula are calculated as below.

$Section\;Formula=\left(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\right)$

$Coordinates\;of\;C=\left(\frac{1\times 6+3\times 2}{1+3},\frac{1\times 8+3\times 4}{1+3}\right)$

$Coordinates\;of\;C=\left(\frac{6+6}{4},\frac{8+12}{4}\right)$

$Coordinates\;of\;C=\left(\frac{12}{4},\frac{20}{4}\right)$

$Coordinates\;of\;C=(3,5)$

6. Coordinates of C from the graph paper and from section formula are SAME.

Result

$Section\;Formula=\left(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\right)$ is verified .

Applications

This formula is used to find the centroid of a triangle in geometry, vector algebra and 3–dimensional geometry.

THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW

Search This Blog

Lesson Plan

Featured Posts on Lesson Plan

Mathematics Lab Activity-20 Class X | Probability