Sure, let's solve this step by step:
1. Initial Position:
- Madhuri starts at the origin, which we can denote as (0,0).
2. First Movement:
- Madhuri travels 14 km west. Moving west decreases the x-coordinate.
- Therefore, her new position is (0 - 14, 0) = (-14, 0).
3. Second Movement:
- Madhuri then turns left and travels 6 km south. Turning left from west means she will now be heading south.
- Moving south decreases the y-coordinate.
- Therefore, her new position is (-14, 0 - 6) = (-14, -6).
4. Third Movement:
- Madhuri turns left again and travels 26 km east. Turning left from south means she will now be heading east.
- Moving east increases the x-coordinate.
- Therefore, her new position is (-14 + 26, -6) = (12, -6).
5. Calculating Distance from the Starting Point:
- The final step is to find the distance between her new position (12, -6) and the starting point (0, 0).
- We use the distance formula for this, which is: \
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
- Plugging in the coordinates (12, -6) and (0, 0), we get:
[tex]\[
\text{Distance} = \sqrt{(12 - 0)^2 + (-6 - 0)^2} = \sqrt{12^2 + (-6)^2} = \sqrt{144 + 36} = \sqrt{180} \approx 13.416
\][/tex]
Hence, Madhuri is approximately 13.416 kilometers away from the starting point.
