Question

Point A is located at (1,10) and point B is located at (20,18). What point partitions the direction line segment AB inot a 2:5 ratio?

Answer 1

Given a segment joining the points A = (1, 10) and B = (20, 18).

To find the point (a, b) that partitions the segment AB into a 2:5 ratio, we use the equations:

`\begin{gathered} (a-1)/(20-a)=(2)/(5)\ldots(1) \\ (b-10)/(18-b)=(2)/(5)\ldots(2) \end{gathered}`

That is, the 2:5 ratio also holds for the x and y coordinates. Solving equation (1) for a:

`\begin{gathered} 5(a-1)=2(20-a) \\ 5a-5=40-2a \\ 7a=45 \\ a=(45)/(7)=6(3)/(7) \end{gathered}`

Now, solving equation (2) for b:

`\begin{gathered} 5(b-10)=2(18-b) \\ 5b-50=36-2b \\ 7b=86 \\ b=(86)/(7)=12(2)/(7) \end{gathered}`

So the point is:

`(6(3)/(7),12(2)/(7))`