Question

Determine the length of the line segment UV, with U(3,-5) and V(-5,-9) Give your answer in simplified radical form.

Answer 1

The length of the line segment between two points (x1, y1) and (x2, y2) is given by:

$L=\sqrt{\lparen x_2-x_1)^2+\operatorname{\lparen}y_2-y_1)^2}$

The line segment UV has the endpoints U(3, -5) and (-5, -9). Substituting:

$L=\operatorname{\lparen}-5-3)^2+\operatorname{\lparen}-9+5)^2$$\begin{gathered} L=\sqrt{\left(-8\right)^2+\left(-4\right)^2} \\ L=\sqrt{64+16} \\ L=\sqrt{80} \end{gathered}$

It's required to express the answer in simplified radical form, so we can rewrite the radicand as 80 = 16 * 5:

$\begin{gathered} L=\sqrt{16\cdot5} \\ L=\sqrt{16}\cdot\sqrt{5} \\ L=4\sqrt{5} \end{gathered}$