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: 29

Answer

(a) Refer to the image below for the plot. (b) Distance between the two points =$4\sqrt{10}\approx 12.65$ units (c) Midpoint of the segment joining the two points: $(0, 0)$

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: $d=\sqrt{[6-(-6)]^2+(-2-2)^2} \\d=\sqrt{12^2+(-4)^2} \\d=\sqrt{144+16} \\d=\sqrt{160} \\d=\sqrt{16(10)} \\d=4\sqrt{10} \\d\approx 12.65$ (c) Find the mmidpoint 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 = $\left(\frac{6+(-6)}{2}, \frac{-2+2}{2}\right)=(0,0)$
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