Question

Find the length of the line segment whose endpoints are (-8,7) and
(6,4).

Answer 1

`\underline{\underline{\large\bf{Given:-}}}`

`\red{\leadsto}\:`
`\textsf{}`
`\sf Endpoints \:of \: line \: segment \:are \:(-8,7)`

`\sf and \:(6,4)`

`\underline{\underline{\large\bf{To Find:-}}}`

`\orange{\leadsto}\:`
`\textsf{Length of the line}`
`\sf`

`\\`

`\underline{\underline{\large\bf{Solution:-}}}\\`

>>Let us consider these points on a line segment AB such that point A and B lies on opposite ends

`\\A( - 8,7) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B(6,4)\\ \bull \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{} \bull \\`

We will find distance between points by distance formula-

`\red{\underline{\boxed{\sf{Distance=√((x_2-x_1)^2+(y_2-y_1)^2)}}}}`

Here-

• 
  `\sf x_2 = 6`
• 
  `\sf x_1 = -8`
• 
  `\sf y_2 = 4`
• 
  `\sf y_1 = 7`

Putting Values:-

`\begin{gathered}\\\longrightarrow\quad \sf AB = \sqrt{(6 - (-8)) ^(2) + (4-7) ^(2) } \\\end{gathered}`

`\begin{gathered}\\\longrightarrow\quad \sf √((6+8)^2 + (-3)^2) \\\end{gathered}`

`\begin{gathered}\\\longrightarrow\quad \sf √(14^2+ (-3)^2 ) \\\end{gathered}`

`\begin{gathered}\\\longrightarrow\quad \sf √(196+ 9 ) \\\end{gathered}`

`\begin{gathered}\\\longrightarrow\quad \sf √(205) \\\end{gathered}`

`\longrightarrow \sf length \:of \: the \: line \:segment \:whose \: \:`

`\sf endpoints \;are \: (-8,7) \:and \:(6,4) \:is \: √(205) \;units`