{"id":1604,"date":"2021-12-02T19:38:44","date_gmt":"2021-12-03T00:38:44","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-2\/"},"modified":"2022-11-02T10:36:53","modified_gmt":"2022-11-02T14:36:53","slug":"answer-key-3-2","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-2\/","title":{"raw":"Answer Key 3.2","rendered":"Answer Key 3.2"},"content":{"raw":"
    \n \t
  1. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(6--6)^2&+&(4--1)^2 \\\\\nd^2&=&12^2&+&5^2 \\\\\nd^2&=&144&+&25 \\\\\nd^2&=&169&& \\\\\nd^2&=&\\sqrt{169}&& \\\\\nd&=&13&&\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(5-1)^2&+&(-1--4)^2 \\\\\nd^2&=&4^2&+&3^2 \\\\\nd^2&=&16&+&9 \\\\\nd^2&=&25&& \\\\\nd^2&=&\\sqrt{25}&& \\\\\nd&=&5&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(3--5)^2&+&(5--1)^2 \\\\\nd^2&=&8^2&+&6^2 \\\\\nd^2&=&64&+&36 \\\\\nd^2&=&100&& \\\\\nd^2&=&\\sqrt{100}&& \\\\\nd&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(12-6)^2&+&(4--4)^2 \\\\\nd^2&=&6^2&+&8^2 \\\\\nd^2&=&36&+&64 \\\\\nd^2&=&100&& \\\\\nd^2&=&\\sqrt{100}&& \\\\\nd&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(4--8)^2&+&(3--2)^2 \\\\\nd^2&=&12^2&+&5^2 \\\\\nd^2&=&144&+&25 \\\\\nd^2&=&169&& \\\\\nd^2&=&\\sqrt{169}&& \\\\\nd&=&13&&\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(7-3)^2&+&(1--2)^2 \\\\\nd^2&=&4^2&+&3^2 \\\\\nd^2&=&16&+&9 \\\\\nd^2&=&25&& \\\\\nd^2&=&\\sqrt{25}&& \\\\\nd&=&5&&\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(-2--10)^2&+&(0--6)^2 \\\\\nd^2&=&8^2&+&6^2 \\\\\nd^2&=&64&+&36 \\\\\nd^2&=&100&& \\\\\nd^2&=&\\sqrt{100}&& \\\\\nd&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{lllll}\nd^2&=&(14-8)^2&+&(6--2)^2 \\\\\nd^2&=&6^2&+&8^2 \\\\\nd^2&=&36&+&64 \\\\\nd^2&=&100&& \\\\\nd^2&=&\\sqrt{100}&& \\\\\nd&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n \t
  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]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    2. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    3. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    4. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    5. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    6. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    7. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    8. [latex]d^2\\quad=\\quad\\Delta x^2+\\Delta y^2[\/latex]
      \n[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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n
    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]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":24,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1604","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1604","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1604\/revisions"}],"predecessor-version":[{"id":1605,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1604\/revisions\/1605"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1604\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1604"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1604"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1604"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}