Question

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

Answer 1

Answer:

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

• $\:d=2\sqrt{5}$  

Step-by-step explanation:

Given the points

• (-8,-2)

• (-6,2)

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

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

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

  $=\sqrt{\left(-6-\left(-8\right)\right)^2+\left(2-\left(-2\right)\right)^2}$

  $=\sqrt{\left(-6+8\right)^2+\left(2+2\right)^2}$

  $=\sqrt{2^2+4^2}$

  $=\sqrt{20}$

  $=\sqrt{2^2\cdot \:5}$

  $=\sqrt{5}\sqrt{2^2}$          ∵ $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

  $=2\sqrt{5}$              ∵  $\sqrt[n]{a^n}=a$

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

• $\:d=2\sqrt{5}$