Question

Line segment AB has endpoints A(1,4) and B(6,2). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 2:3

Answer 1

(3,16/5)

Explanation:

(2)(6)+(3)(1)/(2+3),(2)(2)+(3)(4)/(2+3)=3,16/5

Answer 2

`(3,3(1)/(5))`

Explanation:

We use the formula;

`((mx_2+nx_1)/(2),(my_2+ny_1)/(2))`

where m:n=2:3 and
`x_1=1,x_2=6,y_1=4,y_2=2`

We substitute these values to get;

`((2(6)+3(1))/(2+3),(2(2)+3(4))/(2+3))`

We simplify to get:

`((15)/(5),(16)/(5))`

`(3,3(1)/(5))`