Question

The endpoints of a line segment AR are A(8,-2) and R(-4,1). What is the length of the AR?

Answer 1

Answer:

The length of the AR is  $3\sqrt{17}$  or $12.4$ units.

Step-by-step explanation:

Given the endpoints of a line segment AR

• A(8, -2)

• R(-4, 1)

We can calculate the length of AR using the formula

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

In our case,

• (x₁, y₁) = (8, -2)  

• (x₂, y₂) = (-4, 1)

Substituting (x₁, y₁) = (8, -2) and (x₂, y₂) = (-4, 1) in the formula

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

        $=\sqrt{\left(-4-8\right)^2+\left(1-\left(-2\right)\right)^2}$

        $=\sqrt{\left(-4-8\right)^2+\left(1+2\right)^2}$            ∵ Apply rule:  $-\left(-a\right)=a$

        $=\sqrt{12^2+3^2}$

        $=\sqrt{144+9}$

        $=\sqrt{153}$

        $=\sqrt{9\times 17}$

         $=\sqrt{17}\sqrt{3^2}$          Apply radical rule:   $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

         $=3\sqrt{17}$              Apply radical rule:   $\sqrt[n]{a^n}=a$

         $=12.4$

Therefore, the length of the AR is  $3\sqrt{17}$  or $12.4$ units.