Chapter 9.5, Problem 43E

To determine

Tocompare:Length of given line segments

Answer to Problem 43E

$\overline{PQ}$ is longer than $\overline{AB}$

Explanation of Solution

Given information:

End points of $\overline{AB}$ are $A\left(-1,-2\right)\text{ and }B\left(6,1\right)$

End points of $\overline{PQ}$ are $P\left(1,1\right)\text{ and }Q\left(6,7\right)$

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 $\overline{AB}$

  $\begin{array}{l}\overline{AB}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(6-\left(-1\right)\right)}^2+{\left(1-\left(-2\right)\right)}^2}\\ =\sqrt{{\left(7\right)}^2+{\left(3\right)}^2}\\ =\sqrt{49+9}\\ =\sqrt{58}\end{array}$

Length of $\overline{PQ}$

  $\begin{array}{l}\overline{PQ}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(6-1\right)}^2+{\left(7-1\right)}^2}\\ =\sqrt{{\left(5\right)}^2+{\left(6\right)}^2}\\ =\sqrt{25+36}\\ =\sqrt{61}\end{array}$

Therefore, we can say that $\overline{PQ}$ is longer than $\overline{AB}$