Question

27.) Find the sum of the length of line segments EF and CD.JGV6A 140AB 5/10C 1300KD 234E8D

Answer 1

Let's find the length of EF:

`\begin{gathered} EF=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ EF=\sqrt[]{(8-(-1))^2+(-4-(-1))^2} \\ EF=\sqrt[]{(9)^2+(-3)^2} \\ EF=\sqrt[]{90}=3\sqrt[]{10} \end{gathered}`

Now, let's find the length of CD:

`\begin{gathered} CD=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ CD=\sqrt[]{(-7-(-1))^2+\mleft(-4-\mleft(-2\mright)\mright)^2} \\ CD=\sqrt[]{(-6)^2+(-2)^2} \\ CD=\sqrt[]{40}=2\sqrt[]{10} \end{gathered}`

Therefore:

`\begin{gathered} EF+CD=3\sqrt[]{10}+2\sqrt[]{10}=5\sqrt[]{10} \\ \text{Answer:} \\ 5\sqrt[]{10} \end{gathered}`