Answer:
5√10
Step-by-step explanation:
The distance between two points A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) on the coordinate plane is given by:
[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 }[/tex]
From the image attached the coordinates of the points are E(-1, -1), F(8, -4), C(-7, -4) and D(-1, 2).
Hence the lengths of the line segment EF and CD are:
[tex]|EF|=\sqrt{(8-(-1))^2+(-4-(-1))^2} =\sqrt{90}=3\sqrt{10} \\\\CD=\sqrt{(-1-(-7))^2+(-2-(-4))^2}=\sqrt{40} =2\sqrt{10} \\\\Therefore:\\\\|EF|+|CD|=3\sqrt{10} +2\sqrt{10} =5\sqrt{10}[/tex]
