Chapter 7 · Question 5

Derive the midpoint formula from the section formula.

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)

.

The midpoint is the average of the two

x

-coordinates and the two

y

-coordinates.

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)

.