Mathematics, 17.07.2019 12:30 thicklooney
The coordinates of the vertices of a polygon are (−4, 2) , (2, 2) , (2, −1) , (−2, −3) , and (−5, −2) . what is the perimeter of the polygon? enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
Answers: 1
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -4}}\quad ,&{{ 2}})\quad % (c,d) &({{ -5}}\quad ,&{{ -2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[-5-(-4)]^2+[-2-2]^2}\implies d=\sqrt{(-5+4)^2+(-4)^2} \\\\\\ d=\sqrt{(-1)^2+(-4)^2}\implies d=\sqrt{1+16}\implies \boxed{d=\sqrt{17}}\\\\ -------------------------------](/tpl/images/0100/1352/41fc3.png)
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (c,d) &({{ -5}}\quad ,&{{ -2}}) % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad \end{array}\qquad \\\\\\ d=\sqrt{[-2-(-5)]^2+[-3-(-2)]^2}\\\\\\ d=\sqrt{(-2+5)^2+(-3+2)^2} \\\\\\ d=\sqrt{3^2+(-1)^2}\implies d=\sqrt{9+1}\implies \boxed{d=\sqrt{10}}\\\\ -------------------------------\\\\ ](/tpl/images/0100/1352/2806c.png)
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ 2}}\quad ,&{{ -1}}) \end{array}\qquad \\\\\\ d=\sqrt{[2-(-2)]^2+[-1-(-3)]^2}\implies d=\sqrt{(2+2)^2+(-1+3)^2} \\\\\\ d=\sqrt{4^2+2^2}\implies d=\sqrt{16+4}\implies d=\sqrt{20}\implies \boxed{d=2\sqrt{5}}](/tpl/images/0100/1352/70078.png)
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