Question

Find the coordinates of P so that P partitions the segment AB in the ratio 5:1 given the points A(2, 4) and B(8, 10).

Answer 1

Answer:

P = (7 , 9)

Step-by-step explanation:

Given ,

'P' divides line segment 'AB' in the ratio 5 : 1

A = (2 , 4)

B = (8 , 10)

To Find :-

Co-ordinates of point of 'P'

Formula Required :-

Section(Internal Division) formula :-

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

Solution :-

Let ,

m : n = 5 : 1

A = (2 , 4)

Let,

x_1 = 2 , y_1 = 4

B = (8 , 10)

Let,

x_2 = 8 , y_2 = 10

Substituting in formula :-

$P=\left(\dfrac{5(8)+1(2)}{5+1},\dfrac{5(10)+1(4)}{5+1}\right)$

$=\left(\dfrac{40+2}{6},\dfrac{50+4}{6}\right)$

$=\left(\dfrac{42}{6},\dfrac{54}{6}\right)$

= (7 , 9)

∴ Co-ordinates of 'P' = (7 , 9)