What is the shortest distance between points W and Y? Study the following information carefully and answer the questions given below:

Riya starts walking from point Z towards west for 11m to reach point Y. Then, she turns right and walks for 4m to reach point X. Then she again turns right and walks for 14m to reach point W and then finally she turns towards south and walks for 6m to reach point V.

Karan starts walking towards north for 2m from point Z to reach at point U. Then, he takes right and left turn and walks for 6m and 9m to reach point T and S respectively. Then, he takes left turn and walks for 5m to reach point R. -

Correct Answer: $2\sqrt{53}$ m

Step-by-Step Explanation:

1. Trace Riya's Movement:

• Starting from point Z, Riya walks 11 m towards West to reach point Y.
So, point Y is 11 m West of point Z.

• From point Y, she turns right (which is North) and walks 4 m to reach point X.
So, point X is 4 m North of point Y.

• From point X, she turns right (which is East) and walks 14 m to reach point W.
So, point W is 14 m East of point X.

2. Analyze the Position of Point W relative to Point Y:

To go from point Y to point W:

• Move North by 4 m (vertical distance, Δy = 4 m).

• Move East by 14 m (horizontal distance, Δx = 14 m).

3. Calculate the Shortest Distance between W and Y:

The shortest distance between two points is given by the straight-line distance using the Pythagorean theorem:

$\text{Distance}=\sqrt{{\left(\mathrm{\Delta x}\right)}^2+{\left(\mathrm{\Delta y}\right)}^2}$

Substitute Δx = 14 m and Δy = 4 m into the formula:

$\text{Distance}=\sqrt{{14}^2+4^2}$

$\text{Distance}=\sqrt{196+16}$

$\text{Distance}=\sqrt{212}$

Simplify the radical:

$\sqrt{212}=\sqrt{4\times 53}=2\sqrt{53}\text{m}$

Thus, the shortest distance between points W and Y is $2\sqrt{53}$ m.