Question

Use the distance formula to determine the lengths of DE and AC.

Answer 1

Given:

The given coordinates are

`\begin{gathered} A(x_1,y_1) \\ C(x_3,y_3) \\ D=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ E=((x_3+x_2)/(2),(y_3+y_2)/(2)) \end{gathered}`

Required:

We need to find the length of DE and AC

Step-by-step explanation:

By using distance formula

`AC=√((x_1-x_3)^2+(y_1-y_3)^2)`

now for DE

`\begin{gathered} DE=\sqrt{((x_1+x_2)/(2)-(x_3+x_2)/(2))^2+((y_1+y_2)/(2)-(y_3+y_2)/(2))^2}^ \\ =\sqrt{((x_1+x_2-x_3-x_(2))^2)/(4)+((y_1+y_2-y_3-y_2)^2)/(4)} \\ =\sqrt{((x_1-x_3)^2)/(4)+((y_1-y_3)^2)/(4)} \end{gathered}`

Final answer: