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: 50

Answer

Distance: 5.4 Midpoint: (-1,0.5)

Work Step by Step

We know that A=(0,3) and B=(-2,-2). To find the distance, use the Distance Formula which is $\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$. Substituting gives $\sqrt {\left( {0 - (-2) } \right)^2 + \left( {3 - (-2) } \right)^2 }=\sqrt {\left( {2 } \right)^2 + \left( {5} \right)^2 }=\sqrt {4+25}=\sqrt {29}=5.4$ To find the midpoint, use the Midpoint Formula which is $(\frac{x_1 + x_2}{2}, \frac {y_1 + y_2}{2})$. Substituting gives $(\frac{0 + (-2)}{2}, \frac {3 + (-2)}{2})=(\frac{-2}{2}, \frac {1}{2})=(-1,0.5)$
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