Question

find the coordinates of a point that divides the line joining the point (3 2) and (4,-2) in the ratio 4:9

Answer 1

Answer:

Co-ordinates of the point = (43/13 , 10/13)

Step-by-step explanation:

Given,

A = (3 , 2)

B = (4 , -2)

Ratio = 4 : 9

To Find :-

Co-ordinates of the point which divides AB in the ratio 4 : 9.

Formula Required :-

Internal division formula :-

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

Ratio = m : n

4 : 9 = m : n

→ m = 4

n = 9

A = (3 , 2)

Let,

x_1 = 3 , y_1 = 2

B = (4 , -2)

Let,

x_2 = 4 , y_2 = -2

Substituting in the formula :-

$Co-ordinates\:of\:the\:point=\left(\dfrac{4(4)+9(3)}{4+9},\dfrac{4(-2)+9(2)}{4+9}\right)$

$=\left(\dfrac{16+27}{13},\dfrac{-8+18}{13}\right)$

= (43/13 , 10/13)

∴ Co-ordinates of the point = (43/13 , 10/13)