First solve for the distance between the 2 ends of the line segment which are (3,2) and (-6,-7).
In short the distance between (3,2) to (-6,-7).
[tex]d= \sqrt{( x_{2}-x_{1})^2+(y_{2}-y_{1})^2 } [/tex]
Given:
[tex]x_{1}=3[/tex]
[tex]y_{1}=2[/tex]
[tex]x_{2}=-6[/tex]
[tex]y_{2}=-7[/tex]
solution:
[tex]D= \sqrt{( -6-3)^2+(-7-2)^2 } [/tex]
[tex]D=9 \sqrt{2} [/tex] or [tex]12.728 units[/tex]
then solve the distance from (3,2) to (-3,-4)
using the same formula:
[tex]d= \sqrt{( x_{2}-x_{1})^2+(y_{2}-y_{1})^2 } [/tex]
solution:
[tex]d_{1}= \sqrt{( -3-3)^2+(-4-2)^2 } [/tex]
[tex]d_{1}=6 \sqrt{2} [/tex] or [tex]8.485 units[/tex]
solve for [tex]d_{2} = D-d_{1}[/tex]
[tex]d_{2} =9 \sqrt{2}-6 \sqrt{2}[/tex]
[tex] d_{2} =3 \sqrt{2} [/tex] or [tex]4.423 units[/tex]
ratio:
[tex]3 \sqrt{2}:6 \sqrt{2} [/tex]
