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: 23

Answer

distance between the two given points = 10 midpoint of the segment joining the two points: $(1, 0)$

Work Step by Step

RECALL: (i) The distance, d, between the points (a, b) and (c, d) can be found using the distance formula: $\\d=\sqrt{(a-c)^2+(b-d)^2}$ (ii) The midpoint of the points (a, b) and (c, d) can be found using the midpoint formula: $\\\text{midpoint} = \left(\frac{a+c}{2}, \frac{b+d}{2}\right)$ The two points are (-3, 3) and (5, -3). Use the formulas above to have: (a) distance between the two points: $=\sqrt{(-3-5)^2+[3-(-3)]^2} \\=\sqrt{(-8)^2+(6)^2} \\=\sqrt{64+36} \\=\sqrt{100} \\=10$ (b) midpoint of the segment that joins them: $\\=\left(\frac{-3+5}{2}, \frac{3+(-3)}{2}\right) \\=\left(\frac{2}{2}, \frac{0}{2}\right) \\=(1, 0)$
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