Geometry: Common Core (15th Edition)

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

Chapter 2 - Reasoning and Proof - Common Core Cumulative Standards Review - Selected Response - Page 136: 20


a) M(6,2) b) 𝘈𝘉= 10

Work Step by Step

1) You are given the points A(3,6) and B(9,-2) 2) We determine the midpoint using the midpoint formula m=$(\frac{x_{1}+x_{2}}{2}$, $\frac{y_{1}+y_{2}}{2})$= $(\frac{3+9}{2}$, $\frac{6-2}{2})$ 3) This simplifies into: $(\frac{12}{2}$, $\frac{4}{2})$= (6, 2) 4) Next, you use distance formula to get the total length of AB d=$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ 5) Plug in the coordinates d=$\sqrt{(9-3)^{2}+(-2-6)^{2}}$=$\sqrt {100}$=10 6) Therefore, the midpoint of line 𝘈𝘉 is at (6,2) and the line's length is 10 units
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