Question

Find the distance between the two points in simplest radical form.
(8, – 7) and (1, -1)

Answer 1

The distance between the two points is
`√(85)` units

Explanation:

Let us revise the rule of the distance between two point
`(x_(1),y_(1))` and
`(x_(2),y_(2))`

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

∵ We need to find the distance between the two points (8, -7) and (1, -1)

→ Let
`x_(1)` = 8 and
`x_(2)` = 1

→ Let
`y_(1)` = -7 and
`y_(2)` = -1

→ Substitute their values in the rule above

∴
`d=\sqrt{(1-8)^(2)+(-1--7)^(2)}`

∴
`d=\sqrt{(-7)^(2)+(-1+7)^(2)}`

∴
`d=√(49+36)`

∴
`d=√(85)`

→ Simplify the radical

∵ 85 = 5 × 17

→ Both of them are prime numbers

∴ The simplest form of
`√(85)` is
`√(85)`

∴ The distance between the two points is
`√(85)` units