Question

What are the coordinates of the point on the directed line segment from (-4,10) to (5,1) that partitions the segment into a ratio of 2 to 1?

Answer 1

Given the points ( -4 , 10 ) and ( 5 , 1 )

(x,y) is the point that partitions the segment into a ratio of 2 to 1

So, the equation to find the coordinates x will be :

`(-4-x)/(x-5)=(2)/(1)`

Solve for x :

`\begin{gathered} 2(x-5)=-4-x \\ 2x-10=-4-x \\ 2x+x=-4+10 \\ 3x=6 \\ \\ x=(6)/(3)=2 \end{gathered}`

The equation to find the coordinates y will be :

`(10-y)/(y-1)=(2)/(1)`

Solve for y :

`\begin{gathered} 2(y-1)=10-y \\ 2y-2=10-y \\ 2y+y=10+2 \\ 3y=12 \\ \\ y=(12)/(3)=4 \end{gathered}`

So, the answer is : the point will be : ( 2 , 4 )