Chapter 7 · Question 4

State the section formula for internal division.

Answer

If

P(x,y)

divides

A(x_1,y_1)

and

B(x_2,y_2)

internally in the ratio

m:n

, then

x=\frac{mx_2+nx_1}{m+n}

and

y=\frac{my_2+ny_1}{m+n}

.

Section formula gives coordinates of a point dividing a segment in a given ratio.

For internal division in the ratio

AP:PB=m:n

, the coordinates are

P\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)

. The weights are crossed:

m

is multiplied with the coordinates of

B

, and

n

with coordinates of

A

.

If $P(x,y)$ divides $A(x_1,y_1)$ and $B(x_2,y_2)$ internally in the ratio $m:n$ , then $x=\frac{mx_2+nx_1}{m+n}$ and $y=\frac{my_2+ny_1}{m+n}$ .