Given:
The given coordinates are
[tex]\begin{gathered} A(x_1,y_1) \\ C(x_3,y_3) \\ D=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ E=(\frac{x_3+x_2}{2},\frac{y_3+y_2}{2}) \end{gathered}[/tex]
Required:
We need to find the length of DE and AC
Explanation:
By using distance formula
[tex]AC=\sqrt{(x_1-x_3)^2+(y_1-y_3)^2}[/tex]
now for DE
[tex]\begin{gathered} DE=\sqrt{(\frac{x_1+x_2}{2}-\frac{x_3+x_2}{2})^2+(\frac{y_1+y_2}{2}-\frac{y_3+y_2}{2})^2}^ \\ =\sqrt{\frac{(x_1+x_2-x_3-x_{2)}^2}{4}+\frac{(y_1+y_2-y_3-y_2)^2}{4}} \\ =\sqrt{\frac{(x_1-x_3)^2}{4}+\frac{(y_1-y_3)^2}{4}} \end{gathered}[/tex]
Final answer:
