Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Test - Page 306: 35

Answer

The value of the length and the midpoint of the line segment whose endpoints are $\underline{5}$ and $\underline{\left( \frac{7}{2},0 \right)}$ respectively.

Work Step by Step

Calculate the length of the line segment as follows: $\begin{align} & d=\sqrt{{{\left( 5-2 \right)}^{2}}+{{\left( 2-\left( -2 \right) \right)}^{2}}} \\ & =\sqrt{{{3}^{2}}+{{4}^{2}}} \\ & =\sqrt{25} \\ & =5 \end{align}$ Hence, the length of the line segment is $5$ units. Calculate the midpoint $\left( x,y \right)$ of the line segment as follows: $\begin{align} & x=\frac{2+5}{2} \\ & =\frac{7}{2}. \end{align}$ $\begin{align} & y=\frac{-2+2}{2} \\ & =0. \end{align}$ Hence, the midpoint of the line segment is $\left( \frac{7}{2},0 \right)$.
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