Answer:
The length of the AR is [tex]3\sqrt{17}[/tex] or [tex]12.4[/tex] units.
Step-by-step explanation:
Given the endpoints of a line segment AR
We can calculate the length of AR using the formula
[tex]L_{AB}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
In our case,
Substituting (x₁, y₁) = (8, -2) and (x₂, y₂) = (-4, 1) in the formula
[tex]L_{AB}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(-4-8\right)^2+\left(1-\left(-2\right)\right)^2}[/tex]
[tex]=\sqrt{\left(-4-8\right)^2+\left(1+2\right)^2}[/tex] ∵ Apply rule: [tex]-\left(-a\right)=a[/tex]
[tex]=\sqrt{12^2+3^2}[/tex]
[tex]=\sqrt{144+9}[/tex]
[tex]=\sqrt{153}[/tex]
[tex]=\sqrt{9\times 17}[/tex]
[tex]=\sqrt{17}\sqrt{3^2}[/tex] Apply radical rule: [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]=3\sqrt{17}[/tex] Apply radical rule: [tex]\sqrt[n]{a^n}=a[/tex]
[tex]=12.4[/tex]
Therefore, the length of the AR is [tex]3\sqrt{17}[/tex] or [tex]12.4[/tex] units.
