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Chapter 7 · Question 5

Derive the midpoint formula from the section formula.

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Q5

Derive the midpoint formula from the section formula.

Answer Revealed

Direct Answer:

For midpoint, ratio is

1:1

. Substituting

m=n=1

gives

P\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

.

Simple Explanation

The midpoint is the average of the two

x

-coordinates and the two

y

-coordinates.

Exam-Ready Structure

Using section formula with

m=n=1

,

x=\frac{x_2+x_1}{2}

and

y=\frac{y_2+y_1}{2}

. Hence midpoint of

A(x_1,y_1)

and

B(x_2,y_2)

is

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

.

Key Points

For midpoint, ratio is $1:1$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

Related Questions

Find the point dividing $(1,2)$ and $(7,8)$ internally in the ratio $2:1$ .

State the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ .

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