Section formula — lesson. Mathematics CBSE, Class 10.

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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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We have learnt how to plot the points on a coordinate plane and find the distance between two points.

Now, we will learn how to divide a line segment into two parts.

Do you think is it possible to divide the line segment into two unequal parts?

Yes, a line segment can be divided into two unequal parts using the section formula.

Imagine you have

$6$ milk packets and two bags of unequal sizes.

Bag

$A$ can hold

$4$ milk packets, while bag

$B$ can hold only

$2$ milk packets.

In this case, a total of

$6$ milk packets is distributed across the two bags in the ratio of

$4:2$ .

Similarly, a line segment can also be divided into unequal ratios.

Let us look at how a section formula gets constructed.

In the figure given above, a line segment

$AB$ is divided into two unequal parts in the ratio

$m : n$ .

Let

$A$ be

$x_1$ ,

$P$ be

$x$ and

$B$ be

$x_2$ such that

$x_2 > x > x_1$ .

The co-ordinate of

$P$ divides the line segment in the ratio

$m : n$ .

This means,

$\frac{AP}{PB} = \frac{m}{n}$ .

$\frac{x - x_{1}}{x_{2} - x} = \frac{m}{n}$

$n(x - x_1)$

$=$

$m(x_2 - x)$

$nx - nx_1 = mx_2 - mx$

$mx + nx = mx_2 + nx_1$

$x(m + n) = mx_2 + nx_1$

$x = \frac{m x_{2} + n x_{1}}{m + n}$

$A$ ,

$P$ , and

$B$ has the coordinates

$(x_1$ ,

$y_1)$ ,

$(x$ ,

$y)$ , and

$(x_2$ ,

$y_2)$ respectively, then:

$x = \frac{m x_{2} + n x_{1}}{m + n}$

$y = \frac{m y_{2} + n y_{1}}{m + n}$

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1. Section formula

Theory: