Question

Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

Answer 1

Let P( x , y)   be the point which divide the line segment joining A (2, 3) and B (3, 4) in the ratio 1: 5.

Now according to the section formula if point a point P divides a line segment joining${\displaystyle A(x_1,y_1)}$ and ${\displaystyle B(x_2, y_2)}$ in the ratio m: n internally than,`

${\displaystyle P(x,y)=(\frac{n{x}_1+m{x}_2}{m +n} , \frac{n{y}_1 +m{y}_2}{m+n})}$

Now we will use section formula as,

${\displaystyle P(x,y)=(\frac{5\left(2\right)+3}{5+1},\frac{5\left(3\right)+4}{4+1})}$

            ${\displaystyle =(\frac{13}{6},\frac{19}{6})}$

So co-ordinate of P is   ${\displaystyle =(\frac{13}{6},\frac{19}{6})}$