Question

HELP ASAP

What is the distance, in units, between the points
`(-3, -4)` and
`(4, -5)`? Express your answer in simplest radical form.

Answer 1

Answer

`\boxed{5 √(2) \: \: \:units}`

Step by step explanation

Let the points be A and B

A ( - 3 , - 4 ) ⇒( x₁ , y₁ )

B ( 4 , - 5 )⇒( x₂ , y₂ )

Now, let's find the distance between these points :

Distance =
`\mathsf{ \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) } }`

Plug the values

⇒
`\mathsf{ \sqrt{ {(4 - ( - 3))}^(2) + {( - 5 - ( - 4))}^(2) } }`

Calculate

⇒
`\mathsf{ \sqrt{ {(4 + 3)}^(2) + {( - 5 + 4)}^(2) } }`

⇒
`\mathsf{ \sqrt{ {(7)}^(2) + {( - 1)}^(2) } }`

Evaluate the power

⇒
`\mathsf{ √(49 + 1) }`

Add the numbers

⇒
`\mathsf{ √(50) }`

Simplify the radical expression

⇒
`\mathsf{5 √(2) \: \: units}`

Hope I helped!

Best regards!!

Answer 2

d=5√2 unit

Explanation:

distance between two points d=√(x2-x1)²+(y2-y1)²

two pints (-3,-4) and (4,-5)

d=√(4-(-3)²+(-5-(-4)²

d=√(4+3)²+(-5+4)²

d=√49+1

d=√50

d=√25*2

d=5√2