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 :

$\frac{-4-x}{x-5}=\frac{2}{1}$

Solve for x :

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

The equation to find the coordinates y will be :

$\frac{10-y}{y-1}=\frac{2}{1}$

Solve for y :

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

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