Answer
B
Work Step by Step
use the distance formula to determine the distance from D(2,4) to C(-1,0)
$d_{DC}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{DC}=\sqrt{(-1-2))^2+(0-4))^2}$
simplify in parentheses
$d_{DC}=\sqrt{(-3)^2+(-4)^2}$
simplify
$d_{DC}=\sqrt{9+16}$
$d_{DC}=\sqrt{25}$
$d_{DC}=5$
use the distance formula to determine the distance from C(-1,0) to A(-2,1)
$d_{CA}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{CA}=\sqrt{(-2-(-1)^2+(1-0)^2}$
simplify in parentheses
$d_{CA}=\sqrt{(-1)^2+(1)^2}$
simplify
$d_{CA}=\sqrt{1+1}$
$d_{CA}=\sqrt{2}$
$d_{CA}=1.4$
use the distance formula to determine the distance from A(-2,1) to B(3,1)
$d_{AB}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{AB}=\sqrt{(3-(-2)^2+(1-1)^2}$
simplify in parentheses
$d_{AB}=\sqrt{(5)^2+(0)^2}$
simplify
$d_{AB}=\sqrt{25+0}$
$d_{AB}=\sqrt{25}$
$d_{AB}=5$
use the distance formula to determine the distance from B(3,1) to F(5,2)
$d_{BF}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{BF}=\sqrt{(5-3)^2+(2-1)^2}$
simplify in parentheses
$d_{BF}=\sqrt{(2)^2+(1)^2}$
simplify
$d_{BF}=\sqrt{4+1}$
$d_{BF}=\sqrt{5}$
$d_{BF}=2.2$
use the distance formula to determine the distance from F(5,2) to E(0,3)
$d_{AB}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{AB}=\sqrt{(0-5)^2+(3-2)^2}$
simplify in parentheses
$d_{AB}=\sqrt{(-5)^2+(1)^2}$
simplify
$d_{AB}=\sqrt{25+1}$
$d_{AB}=\sqrt{26}$
$d_{AB}=5.1$
Sum the individual distances to find the total distance.
$d=5+1.4+5+2.2+5.1=18.7$
