Question

Find the distance between the points (2,-9) and (-1,4)

Answer 1

`√(178)` ≈ 13.3

Explanation:

Calculate the distance using the distance formula

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

with (x₁, y₁ ) = (2, - 9) and (x₂, y₂ ) = (- 1, 4)

d =
`√((-1-2)^2+(4+9)^2)`

=
`√((-3)^2+13^2)`

=
`√(9+169)`

=
`√(178)` ≈ 13.3 ( to 1 dec. place )

Answer 2

The answer is

`√(178) \: \: or \: \: 13.34 \: \: units`

Explanation:

The distance between two points can be found by using the formula

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

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(2,-9) and (-1,4)

The distance between them is

`d = \sqrt{ ({2 + 1})^(2) + ({ - 9 - 4})^(2) } \\ = \sqrt{ {3}^(2) + ({ - 13})^(2) } \\ = √(9 + 169) \\`

We have the final answer as

`√(178) \: \: or \: \: 13.34 \: \: units`

Hope this helps you