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olasank [31]
3 years ago
8

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

Mathematics
1 answer:
Anestetic [448]3 years ago
4 0

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.

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