For the points DE, the slope is derived as;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-\lbrack-6\rbrack}{5-\lbrack-5\rbrack} \\ m=\frac{2+6}{5+5} \\ m=\frac{8}{10} \\ m=\frac{4}{5} \\ \text{The distance is derived as;} \\ DE=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ DE=\sqrt[]{(5-\lbrack-5\rbrack)^2+(2-\lbrack-6\rbrack)^2} \\ DE=\sqrt[]{(5+5)^2+(2+6)^2} \\ DE=\sqrt[]{10^2+8^2} \\ DE=\sqrt[]{100+64} \\ DE=\sqrt[]{164} \\ DE=12.8062\ldots \end{gathered}[/tex]For the points FG;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-12-\lbrack-4\rbrack}{-6-4} \\ m=\frac{-12+4}{-10} \\ m=\frac{-8}{-10} \\ m=\frac{4}{5} \\ \text{The distance is derived as follows;} \\ FG=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ FG=\sqrt[]{(-6-4)^2+(-12-\lbrack-4\rbrack)^2} \\ FG=\sqrt[]{(-10^2)+(}-12+4)^2 \\ FG=\sqrt[]{100+(-8)^2} \\ FG=\sqrt[]{100+64} \\ FG=\sqrt[]{164} \\ FG=12.8062\ldots \end{gathered}[/tex]