Roshni starts from Chennai and drives 10 km towards east. She then takes a right turn, drives 15 km, turns right again and drives 13 km. She then takes a right turn and drives 19 km. She takes a final right turn, drives 6 km and stops at Point Z. What is the shortest distance between Point Z and Chennai?

Let's break down Roshni's path into horizontal (East-West) and vertical (North-South) components. Let the starting point (Chennai) be $(0, 0)$.

Step	Action	Direction Facing	Distance (km)	Net Calculation
1	Starts East	East	10	$+10$ East
2	Turns Right	South	15	$-15$ South
3	Turns Right	West	13	$-13$ West
4	Turns Right	North	19	$+19$ North
5	Turns Right	East	6	$+6$ East

Calculate Net Displacement

Horizontal Displacement ($X$): $10 \text{ (East)} - 13 \text{ (West)} + 6 \text{ (East)} = \mathbf{3 \text{ km East}}$

Vertical Displacement ($Y$): $-15 \text{ (South)} + 19 \text{ (North)} = \mathbf{4 \text{ km North}}$

So, Point Z is 3 km East and 4 km North from the starting point.

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You can now use the distance between two points formula (or) think of it like this:

The shortest distance is the straight line connecting the Start (Chennai) and End (Point Z). This forms the hypotenuse of a right-angled triangle with base 3 km and height 4 km.

Using Pythagoras Theorem ($a^2 + b^2 = c^2$):

$\text{Distance}^2 = (\text{Horizontal})^2 + (\text{Vertical})^2$

$\text{Distance}^2 = 3^2 + 4^2$

$\text{Distance}^2 = 9 + 16$

$\text{Distance} = \sqrt{25}$

$\text{Distance} = 5 \text{ km}$