Question

Find the distance between the two points in simplest radical form.
(0, –4) and (-3,-1)

Answer 1

Explanation:

Hey there!

Given;

The points are;(0,-4) and (-3,-1).

Use formula for distance between the two points.

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

Put all values.

`d = \sqrt{( { - 3 - 0)}^(2) + ( { - 1 + 4)}^(2) }`

Simplify to get answer.

`d = √(9 + 9)`

`d = √(18)`

`d = 3 √(2)`

Therefore, the distance is 3√(2) units or 4.24 units.

Hope it helps...

Answer 2

3
`√(2)`

Explanation:

Calculate the distance d using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (- 3, - 1)

d =
`√((-3-0)^2+(-1+4)^2)`

=
`√((-3)^2+3^2)`

=
`√(9+9)`

=
`√(18)`

=
`√(9(2))`

=
`√(9)` ×
`√(2)` = 3
`√(2)`