Question

D(-5, -6). E(5. 2). F(4.-4), G(-6, -12) (Distance & Slope Fontnulas)

Answer 1

For the points DE, the slope is derived as;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(2-\lbrack-6\rbrack)/(5-\lbrack-5\rbrack) \\ m=(2+6)/(5+5) \\ m=(8)/(10) \\ m=(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}`

For the points FG;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(-12-\lbrack-4\rbrack)/(-6-4) \\ m=(-12+4)/(-10) \\ m=(-8)/(-10) \\ m=(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}`