Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.9 - The Coordinate Plane; Graphs of Equations; Circles - 1.9 Exercises - Page 102: 30

Answer

(a) Refer to the image below for the plot. (b) Distance between the two points = $\sqrt{61} \approx 7.81$ units (c) Midpoint of segment joining the two points: $(2.5, -3)$

Work Step by Step

(a) Refer to the attached image in the answer part for the plot. (b) Solve for the distance between the two points using the distance formula $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ to have: $d=\sqrt{(0-5)^2+(-6-0)^2} \\d=\sqrt{(-5)^2+(-6)^2} \\d=\sqrt{25+36} \\d=\sqrt{61} \\d\approx 7.81$ (c) Find the midpoint of the segment that joins them by using the midpoint formula: $\text{midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ Midpoint = $\left(\frac{0+5}{2}, \frac{-6+0}{2}\right)=(2.5,-3)$
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