Given the line segment with endpoints DC
Step 1: Write the coordinates of the points and define the (x,y) values

Step 2: Write the formula for the distance between two points
![\begin{gathered} |DC|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/f8t1qnjln6bktt1gjbkfvbhi1lppogjcj2.png)
Step 3: Substitute the x and y values
![\begin{gathered} |DC|=\sqrt[]{(4-1)^2+(-1-(-2)_{})^2} \\ =\sqrt[]{(3^2)+(1)^2} \\ =\sqrt[]{9+1} \\ =\sqrt[]{10}\text{ units =3.16units} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/tcs4bfctfqwocqs4azfnsw86lj0n53wdej.png)
Hence, the length of the DC is 3.16 units
Or
![\sqrt[]{10}\text{ units}](https://img.qammunity.org/2023/formulas/mathematics/college/byu6kjfpqutpxw4mx7kgvizvpu00jngjpl.png)
Step 4: Use similar procedure for side CD above to obtain side DA

![\begin{gathered} |AD|=\sqrt[]{(1-(-2_{}_{}))^2+(-2-2)^2} \\ =\sqrt[]{(1+2)^2+(-4)^2} \\ =\sqrt[]{3^2+16} \\ =\sqrt[]{9+16^{}} \\ =\sqrt[]{25\text{ }}\text{ =5 units} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/e65n09a87rchtvpxongknxyv76kzurxlcj.png)
![\begin{gathered} |AD|=\sqrt[]{(1-(-2))^2+(-2-2)^2_{}} \\ =\sqrt[]{(1+2)^2+(-4^2)} \\ =\sqrt[]{9+16} \\ =\sqrt[]{25} \\ =5\text{units} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1fpxcwl7dlabwwvfamcjv2oraoob26jz0m.png)
Hence the length of side DA is 5 units
Summary
CD =3.16 units or root 10
DA= 5 units