Answer:
[tex]\huge\boxed{|DE|=10}[/tex]
Step-by-step explanation:
[tex]d_{DE}=\sqrt{(x_E-x_D)^2+(y_E-y_D)^2}\\\\D(-4,\ 2)\to x_D=-4,\ y_D=2\\\\E(4,\ -4)\to x_E=4,\ y_E=-4\\\\\text{substitute}\\\\d_{DE}=\sqrt{(4-(-4))^2+(-4-2)^2}=\sqrt{8^2+(-6)^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]
