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

The length of the AR is
`3√(17)` or
`12.4` units.

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)=√(\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)=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`=√(\left(-4-8\right)^2+\left(1-\left(-2\right)\right)^2)`

`=√(\left(-4-8\right)^2+\left(1+2\right)^2)` ∵ Apply rule:
`-\left(-a\right)=a`

`=√(12^2+3^2)`

`=√(144+9)`

`=√(153)`

`=√(9* 17)`

`=√(17)√(3^2)` Apply radical rule:
`\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

`=3√(17)` Apply radical rule:
`\sqrt[n]{a^n}=a`

`=12.4`

Therefore, the length of the AR is
`3√(17)` or
`12.4` units.