Answer:
The distance between (-8,-2) and (-6,2) is:
Step-by-step explanation:
Given the points
Computing the distance between (x₁, y₁) and (x₂, y₂)
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
substituting (x₁, y₁) = (-8,-2) and (x₂, y₂) = (-6,2)
[tex]=\sqrt{\left(-6-\left(-8\right)\right)^2+\left(2-\left(-2\right)\right)^2}[/tex]
[tex]=\sqrt{\left(-6+8\right)^2+\left(2+2\right)^2}[/tex]
[tex]=\sqrt{2^2+4^2}[/tex]
[tex]=\sqrt{20}[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex] ∵ [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]=2\sqrt{5}[/tex] ∵ [tex]\sqrt[n]{a^n}=a[/tex]
Therefore, the distance between (-8,-2) and (-6,2) is:
