Question

Find the distance between the two points in simplest radical form.

(-8,-2) and (-6,2)
Please answer FAST

Answer 1

The distance between (-8,-2) and (-6,2) is:

• 
  `\:d=2√(5)`

Explanation:

Given the points

• (-8,-2)

• (-6,2)

Computing the distance between (x₁, y₁) and (x₂, y₂)

`d=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

substituting (x₁, y₁) = (-8,-2) and (x₂, y₂) = (-6,2)

`=√(\left(-6-\left(-8\right)\right)^2+\left(2-\left(-2\right)\right)^2)`

`=√(\left(-6+8\right)^2+\left(2+2\right)^2)`

`=√(2^2+4^2)`

`=√(20)`

`=√(2^2\cdot \:5)`

`=√(5)√(2^2)` ∵
`\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

`=2√(5)` ∵
`\sqrt[n]{a^n}=a`

Therefore, the distance between (-8,-2) and (-6,2) is:

• 
  `\:d=2√(5)`