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Answer Key 3.2

  1. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(6--6)^2&+&(4--1)^2 \\ d^2&=&12^2&+&5^2 \\ d^2&=&144&+&25 \\ d^2&=&169&& \\ d^2&=&\sqrt{169}&& \\ d&=&13&& \end{array}[/latex]
  2. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(5-1)^2&+&(-1--4)^2 \\ d^2&=&4^2&+&3^2 \\ d^2&=&16&+&9 \\ d^2&=&25&& \\ d^2&=&\sqrt{25}&& \\ d&=&5&& \end{array}[/latex]
  3. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(3--5)^2&+&(5--1)^2 \\ d^2&=&8^2&+&6^2 \\ d^2&=&64&+&36 \\ d^2&=&100&& \\ d^2&=&\sqrt{100}&& \\ d&=&10&& \end{array}[/latex]
  4. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(12-6)^2&+&(4--4)^2 \\ d^2&=&6^2&+&8^2 \\ d^2&=&36&+&64 \\ d^2&=&100&& \\ d^2&=&\sqrt{100}&& \\ d&=&10&& \end{array}[/latex]
  5. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(4--8)^2&+&(3--2)^2 \\ d^2&=&12^2&+&5^2 \\ d^2&=&144&+&25 \\ d^2&=&169&& \\ d^2&=&\sqrt{169}&& \\ d&=&13&& \end{array}[/latex]
  6. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(7-3)^2&+&(1--2)^2 \\ d^2&=&4^2&+&3^2 \\ d^2&=&16&+&9 \\ d^2&=&25&& \\ d^2&=&\sqrt{25}&& \\ d&=&5&& \end{array}[/latex]
  7. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(-2--10)^2&+&(0--6)^2 \\ d^2&=&8^2&+&6^2 \\ d^2&=&64&+&36 \\ d^2&=&100&& \\ d^2&=&\sqrt{100}&& \\ d&=&10&& \end{array}[/latex]
  8. [latex]d^2\quad=\quad\Delta x^2+\Delta y^2[/latex]
    [latex]\begin{array}[t]{lllll} d^2&=&(14-8)^2&+&(6--2)^2 \\ d^2&=&6^2&+&8^2 \\ d^2&=&36&+&64 \\ d^2&=&100&& \\ d^2&=&\sqrt{100}&& \\ d&=&10&& \end{array}[/latex]
  9. [latex]\left(\dfrac{6+-6}{2}, \dfrac{5+-1}{2}\right)\Rightarrow \left(\dfrac{0}{2}, \dfrac{4}{2}\right) \Rightarrow (0,2)[/latex]
  10. [latex]\left(\dfrac{5+1}{2}, \dfrac{-2+-4}{2}\right)\Rightarrow \left(\dfrac{6}{2}, \dfrac{-6}{2}\right)\Rightarrow (3,-3)[/latex]
  11. [latex]\left(\dfrac{3+-5}{2}, \dfrac{5+-1}{2}\right)\Rightarrow \left(\dfrac{-2}{2}, \dfrac{4}{2}\right)\Rightarrow (-1,2)[/latex]
  12. [latex]\left(\dfrac{12+6}{2}, \dfrac{4+-4}{2}\right)\Rightarrow \left(\dfrac{18}{2}, \dfrac{0}{2}\right) \Rightarrow (9,0)[/latex]
  13. [latex]\left(\dfrac{-8+6}{2}, \dfrac{-1+7}{2}\right)\Rightarrow \left(\dfrac{-2}{2}, \dfrac{6}{2}\right) \Rightarrow (-1,3)[/latex]
  14. [latex]\left(\dfrac{1+3}{2}, \dfrac{-6+-2}{2}\right)\Rightarrow \left(\dfrac{4}{2}, \dfrac{-8}{2}\right) \Rightarrow (2,-4)[/latex]
  15. [latex]\left(\dfrac{-7+3}{2}, \dfrac{-1+9}{2}\right)\Rightarrow \left(\dfrac{-4}{2}, \dfrac{8}{2}\right) \Rightarrow (-2,4)[/latex]
  16. [latex]\left(\dfrac{2+12}{2}, \dfrac{-2+4}{2}\right)\Rightarrow \left(\dfrac{14}{2}, \dfrac{2}{2}\right) \Rightarrow (7,1)[/latex]

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