Question

Find the distance between the points. (−13, 16), (5, −8)

Answer 1

`- 13 = x1`,
`16 = y1`

`5 = x2`,
`- 8 = y2`

Formula for finding distance between two points:

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

`d = \sqrt{(5 + 13 {)}^(2) + (-8 - 16{)}^(2) }`

`d = \sqrt{(18 {)}^(2) + (-24{)}^(2) }`

`d = \sqrt{324{} + 576{} }`

`d = \sqrt{900{} }`

`d = 30` Final answer.

Answer 2

30

Explanation:

Distance Formula

In a 2 dimensional plane, the distance between points (x1, y1) and (x2, y2) is given by the Pythagorean theorem:

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

Here we have (x1, y1) = (-13, 16) and (x2, y2) = (5,-8)

Simply substitute these values into the above equation to get the result

`d = \sqrt {(5 - (-13))^2 + (-8 - 16)^2}\\`

=
`\sqrt {(18)^2 + (-24)^2}`

`= \sqrt {{324} + {576}}`

`= \sqrt {900}`

`= 30` (Answer)