Question

find the coordinates of the point which divides the line segment joining points A(2 , 5) and B(9 , 19) in the ratio 4 : 3​

Answer 1

Step-by-step explanation:

Given:-

The points A(2 , 5) and B(9 , 19)

To find:-

Find the coordinates of the point which divides the line segment joining points A(2 , 5) and

B(9 , 19) in the ratio 4 : 3.

Solution:-

Given points are A(2 , 5) and B(9 , 19)

Let (x1, y1)=A(2,5)=>x1 = 2 and y1 = 5

Let (x2, y2)=B(9,19)=>x2 = 9 and y2 = 19

Given ratio = 4:3

Let m:n = 4:3 =>m =4 and n=3

We know that

The Coordinates of a point P(x,y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m:n is

[(mx2+nx1)/(m+n) , (my2+ny1)/(m+n)]

On Substituting these values in the above formula then

=>P(x,y)=[(4×9+3×2)/(4+3),(4×19+3×5)/(4+3)]

=>P(x,y)=[(36+6)/7,(76+15)/7]

=>P(x,y)=(42/7 , 91/7)

=>P(x,y)=(6,13)

The required point is (6,13)

Answer:-

The coordinates of the required point for the given problem is ( 6 , 13 )

Used formula:-

The Coordinates of a point P(x,y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m:n is

[(mx2+nx1)/(m+n) , (my2+ny1)/(m+n)]