Question

3. find the distance of the line segment with the given end points (5, 1) and (-8, 3)

Answer 1

`\boxed{ \bold{ \huge{ \tt{ √(173 \:)} \: units}}}`

Explanation:

`\star{ \tt{ \: \: Let \: the \: points \: be \: A \: and \: B}}`

`\star{ \tt{ \: Let \: A ( 5 , 1 ) \: be \: ( x1 ,\: y1</p><p>) \: and \: B ( -8 , 3 ) \: be \: ( x2 , y2 )}}</p><p>`

`\sf{ \underline{ finding \: the \: distance \: between \: these \: points}}`

`\boxed{ \underline{ \underline{ \tt{distance \: = \: \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2)}}}}}`

`\hookrightarrow{ \tt{ \sqrt{ {( - 8 - 5)}^(2) + {(3 - 1)}^(2) } }}`

`\hookrightarrow{ \tt{ \sqrt{ {( - 13)}^(2) + {(2)}^(2) } }}`

`\hookrightarrow{ \tt{ √(169 + 4)}}`

`\hookrightarrow{ \boxed{ \tt{ √(173) \: \: units}}}`

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer 2

Explanation:

(x₁ , y₁) = (5 , 1) & (x₂ , y₂) = (-8 , 3)

`Distance = \sqrt{(x_2-x_1)^(2) + (y_2-y_1)^(2)}\\\\ =\sqrt{(-8-5)^(2)+(3-1)^(2)}\\\\=\sqrt{-13)^(2)+2^(2)}\\\\=√(169+4)\\\\=√(173)units`