Chapter 9.5, Problem 44E

To determine

Tocompare:Length of given line segments

Answer to Problem 44E

$\overline{JK}$ is longer than $\overline{MN}$

Explanation of Solution

Given information:

End points of $\overline{MN}$ are $M\left(-3,2\right)\text{ and }N\left(5,0\right)$

End points of $\overline{JK}$ are $J\left(-3,1\right)\text{ and }K\left(3,-5\right)$

Concept Used:

Distance between two points - $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation:

Length of $\overline{MN}$

  $\begin{array}{l}\overline{MN}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(5-\left(-3\right)\right)}^2+{\left(0-2\right)}^2}\\ =\sqrt{{\left(8\right)}^2+{\left(2\right)}^2}\\ =\sqrt{64+4}\\ =\sqrt{68}\end{array}$

Length of $\overline{JK}$

  $\begin{array}{l}\overline{JK}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(3-\left(-3\right)\right)}^2+{\left(-5-1\right)}^2}\\ =\sqrt{{\left(6\right)}^2+{\left(-6\right)}^2}\\ =\sqrt{36+36}\\ =\sqrt{72}\end{array}$

Therefore, we can say that $\overline{JK}$ is longer than $\overline{MN}$