Question

Find the coordinate of the point which divide the line segment joining A(2,3) and B(3,4) in the ratio 2:3

Answer 1

Given-:

Coordinates of the point are A(2,3) and B(3,4) and the ratio of the line segment which is 2:3

So

Here in order to find the the coordinate of the line that divides the line segment AB in the ratio of 2:3 can be found using the section formula,

Section formula is :

$\frac{mx_{1} + nx_{2}}{m + n} = X \\ \frac{my_{1} + ny_{2}}{m + n} = Y$

Where,

m and n are in the ratio 2:3

Now on solving the whole we get,

$= > \frac{2 \times 3 + 3 \times 2}{5} = X \\ = > \boxed{\frac{12}{5} = X} \\ = > \frac{2 \times 4 + 3 \times 3}{5} = Y \\ = > \boxed{\frac{17}{5} = Y}$

So

The required coordinates are :

12/5 and 17/5

Answer 2

Answer:

Point A = (2,3)

Point B = ( 3,4 )

Ratio = 2:3

Using Section formula,

x = $\mathsf{\dfrac{m_1 x_2 + m_2 x_1}{m_1 + m_2}}$

x = $\mathsf{\dfrac{2*3 + 3*2}{2 + 3 }}$

x = $\mathsf{\dfrac{12}{5}}$

x = 2.4

For y,

y = $\mathsf{\dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2}}$

y = $\mathsf{\dfrac{2*4 + 3*3}{2 + 3 }}$

y = $\mathsf{\dfrac{17}{5}}$

y = 3.4

Coordinates of the point are ( 2.4, 3.4 ).