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suter [353]
3 years ago
14

What is the perimeter of trapezoid JKLM? j -7,4 k -4,4 m -8,3 l -2,3

Mathematics
1 answer:
kompoz [17]3 years ago
8 0
Check the picture below.

you can pretty much just count off the grid the units for JK and MI.

now, let's check how long are KI and JM

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
K&({{ -4}}\quad ,&{{ 4}})\quad 
%  (c,d)
I&({{ -2}}\quad ,&{{ 3}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
KI=\sqrt{[-2-(-4)]^2+[3-4]^2}\implies KI=\sqrt{(-2+4)^2+(3-4)^2}
\\\\\\
KI=\sqrt{2^2+(-1)^2}\implies KI=\sqrt{4+1}\implies \boxed{KI=\sqrt{5}}\\\\
-------------------------------

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
J&({{ -7}}\quad ,&{{ 4}})\quad 
%  (c,d)
M&({{ -8}}\quad ,&{{ 3}})
\end{array}\qquad 
%  distance value
\\\\\\
JM=\sqrt{[-8-(-7)]^2+[3-4]^2}\implies JM=\sqrt{(-8+7)^2+(3-4)^2}
\\\\\\
JM=\sqrt{(-1)^2+(-1)^2}\implies \boxed{JM=\sqrt{2}}

so, add all sides, and that's the perimeter of the trapezoid.

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