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: 22

Answer

distance between the two points = 5 midpoint of the segment joining the two points: $(0, 0.5)$

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 (-2, -1) and (2, 2). Use the formulas above to have: (a) distance between the two points: $=\sqrt{(-2-2)^2+(-1-2)^2} \\=\sqrt{(-4)^2+(-3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5$ (b) midpoint of the segment that joins them: $\\=\left(\frac{-2+2}{2}, \frac{-1+2}{2}\right) \\=(0, 0.5)$
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