Question

find the point which divides the line segment joining the point (3,5) and (9,10) internally in ratio 2:3​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

The points (3,5) & (9,10)  internally in ratio 2:3 .

$\underline{\bf{Explanation\::}}$

As we know that formula of the co-ordinate by internal division;

$\boxed{\bf{\bigg(\frac{mx_2 +nx_1}{m+n} ,\frac{my_2 + ny_1}{m+n}\bigg) }}$

A/q

Let the point C = C(x,y) divide the given line AB in the ratio 2:3.

m:n = 2:3

$\longrightarrow\tt{x = \dfrac{mx_2 + nx_1}{m+n} }$

$\longrightarrow\tt{x = \dfrac{2 \times 9 + 3\times 3}{2+3} }$

$\longrightarrow\tt{x = \dfrac{18 + 9}{5} }$

$\longrightarrow\tt{x = \cancel{\dfrac{27}{5} }}$

$\longrightarrow\bf{x = 5.4}$

&

$\longrightarrow\tt{y = \dfrac{my_2 + ny_1}{m+n} }$

$\longrightarrow\tt{y = \dfrac{2 \times 10 + 3\times 5}{2+3} }$

$\longrightarrow\tt{x = \dfrac{20+15}{5} }$

$\longrightarrow\tt{y = \cancel{\dfrac{35}{5} }}$

$\longrightarrow\bf{y = 7}$

Thus,

The co-ordinate of point C will be (5.4, 7) .