Geometry: Common Core (15th Edition)

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

Chapter 1 - Tools of Geometry - Chapter Test: 8

Answer

x=11 y=19 The distance formula shows the MC=MD.

Work Step by Step

a) use the midpoint formula $M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ substitute $M(\frac{5+17}{2},\frac{9+29}{2})$ $M(\frac{22}{2},\frac{38}{2})$ $M(11,19)$ b) use the distance formula to show the distance is the same from the midpoint to each endpoint. $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d=\sqrt{(5-11)^2+(9-19)^2}$ $d=\sqrt{(-6)^2+(-10)^2}$ $d=\sqrt{36+100}$ $d=\sqrt{136}$ $d=11.7\checkmark$ $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d=\sqrt{(17-11)^2+(29-19)^2}$ $d=\sqrt{(6)^2+(10)^2}$ $d=\sqrt{36+100}$ $d=\sqrt{136}$ $d=11.7\checkmark$
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