College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Cumulative Review: 15

Answer

Distance = $5\sqrt2$ units Midpoint: $(1.5, 0.5)$

Work Step by Step

RECALL: (1) The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ (2) The midpoint of the two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ Use the formulas above to obtain: $d=\sqrt{(-1-4)^2+[3-(-2)]^2} \\d=\sqrt{(-5)^2+(5)^2} \\d=\sqrt{25+25} \\d=\sqrt{50} \\d=\sqrt{25(2)} \\d=\sqrt{5^2(2)} \\d=5\sqrt2$ Midpoint: $=\left(\dfrac{-1+4}{2}, \dfrac{3+(-2)}{2}\right)=(1.5, 0.5)$
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