Respuesta :
SOLUTION
The length of the line segment will be calculated using the distance formula
The distance formula is given as
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The line segment have the points U(3,-5) and V(-5,-9)
Therefoore the length of the line segment is:
[tex]UV=\sqrt{(-5-3)^2+(-9-(-5))^2}[/tex]Calculate the value:
[tex]\begin{gathered} UV=\sqrt{(8)^2+(-4)^2} \\ UV=\sqrt{64+16} \\ UV=\sqrt{80} \\ UV=4\sqrt{5} \end{gathered}[/tex]Therefore the length of the line segment is
[tex]4\sqrt{5}[/tex]The equation of the line segment wil be determined using
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Therefore using the given points the equation of the line is:
[tex]\begin{gathered} y-(-5)=\frac{-9-(-5)}{-5-3}(x-3) \\ y+5=\frac{-4}{-8}(x-3) \\ y+5=\frac{1}{2}x-\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2}-5 \\ y=\frac{1}{2}x-\frac{13}{2} \end{gathered}[/tex]Therefore the equation of the line segment is:
[tex]y=\frac{1}{2}x-\frac{13}{2}[/tex]