Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 1 - Tools of Geometry - 1-7 Midpoint and Distance in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 56: 64


a) $R(-8,9)$ b) 17.9

Work Step by Step

a) Use the midpoint formula: $M_x=\frac{x_1+x_2}{2}$ $-4=\frac{x_R+0}{2}$ $-4\times2=\frac{x_R+0}{2}\times2$ $-8=x_R$ $M_y=\frac{y_1+y_2}{2}$ $1=\frac{y_R+(-7)}{2}$ $1\times2=\frac{y_R+(-7)}{2}\times2$ $2=y_R-7$ $2+7=y_R-7+7$ $9=y_R$ b) Use the distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d=\sqrt{(0-(-8))^2+(-7-9)^2}$ $d=\sqrt{(8)^2+(-16)^2}$ $d=\sqrt{64+256}$ $d=\sqrt{320}$ $d\approx17.9$
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