Question

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

Answer 1

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.