Question

Find the coordinates of the point on the directed segment from (1,2) to (6,12) that divides it into a ratio of 2:3

Answer 1

Point of contact ( 3,6)

Explanation:

Step(i):-

Given that the points are (1,2) and (6,12)

The ratio 2:3 divides the line segment

The line segment divides m:n externally

`((mx_(2)-nx_(1) )/(m-n) ,(mx_(2)-nx_(1) )/(m-n) )`

Step(ii):-

(x₁, y₁) = (1,2) and (x₂, y₂)= (6,12) and m:n =2:3

`((2(6)+3(1) )/(2+3) ,(2(12)+3(2) )/(2+3) )`

(
`((12+3)/(5) ,(24+6)/(5) )`

(
`(15)/(5) ,(30)/(5))`

(3 , 6)

Final answer:-

Point of contact ( 3,6)