Respuesta :
[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Endpoints \:of \: line \: segment \:are \:(-8,7) [/tex]
[tex]\sf and \:(6,4) [/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{Length of the line} [/tex][tex]\sf [/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
>>Let us consider these points on a line segment AB such that point A and B lies on opposite ends
[tex] \\A( - 8,7) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B(6,4)\\ \bull \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{} \bull \\[/tex]
We will find distance between points by distance formula-
[tex]\red{\underline{\boxed{\sf{Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}}}[/tex]
Here-
- [tex]\sf x_2 = 6[/tex]
- [tex]\sf x_1 = -8[/tex]
- [tex]\sf y_2 = 4[/tex]
- [tex]\sf y_1 = 7[/tex]
Putting Values:-
[tex]\begin{gathered}\\\longrightarrow\quad \sf AB = \sqrt{(6 - (-8)) ^{2} + (4-7) ^{2} } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{(6+8)^2 + (-3)^2} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{14^2+ (-3)^2 } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{196+ 9 } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{205} \\\end{gathered} [/tex]
[tex]\longrightarrow \sf length \:of \: the \: line \:segment \:whose \: \: [/tex]
[tex]\sf endpoints \;are \: (-8,7) \:and \:(6,4) \:is \: \sqrt{205} \;units [/tex]
