Question

If a = (-1,-3) and b = (11,8), what is the length of ab?

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{16.27 \: \: units}}}}}`

Explanation:

Given,

A ( - 1 , - 3 )⇒( x₁ , y₁ )

B ( 11 , 8 )⇒( x₂ , y₂ )

Using distance formula to find the length of AB

`\sf{ \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) } }`

plug the values

⇒
`\sf{ \sqrt{ {(11 - ( - 1))}^(2) + {( 8 - ( - 3))}^(2) } }`

We know that
`\sf{( - ) * ( - ) = ( + )}`

⇒
`\sf{ \sqrt{ {(11 + 1)}^(2) + {(8 + 3)}^(2) } }`

Add the numbers

⇒
`\sf{ \sqrt{ {12}^(2) + {11}^(2) } }`

Evaluate the power

⇒
`\sf{ √(144 + 121) }`

Add the numbers and calculate

⇒
`\sf{√(265) }`

⇒
`\sf{16.27}` units

Hope I helped!

Best regards!!