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$

(1){\text{ 40 m}} \\

{\text{(2) 30 m}} \\

{\text{(3) 50 m}} \\

{\text{(4) 55 m}} \\

$

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Applying the Pythagoras theorem in the triangle ABC to determine the value of the distance between the points A and X.

Consider the distance between the points A and C be x.

$ A{C^2} = A{B^2} + B{C^2} \\

{x^2} = {10^2} + {20^2} \\

{x^2} = 100 + 400 \\

x = \sqrt {500} \\

= 10\sqrt 5 \\

= 10 \times 2.236 \\

= 22.36{\text{ meters}} \\ $

Now, to calculate the distance between the starting point and the endpoint $20\sqrt 2 = 20 \times 1.414 = 28.28{\text{ meters}}$ will be added to the value 22.36 meters.

$ D = 28.28 + 22.36 \\

= 50.64{\text{ meters}} \\ $

As we are doing with the approximations in the calculation, the nearest value to the number 50.64 meters given in the option is 50 meters. Hence, the distance between the starting point and the endpoint is 50 meters.