A cat is chasing a mouse. The cat first moves 25 m towards the north, then takes a right turn and moves 100 m, then turns towards the south and moves 25 m further, and finally turns left and moves 55 m. What is the straight line distance between the initial position and the final position of the cat?

Introduction / Context:
This is a path based direction question that ends with a request for the straight line distance between the starting and ending positions. The cat moves along a rectangular path with an additional horizontal leg at the end. Identifying the net displacement and calculating the direct distance between the two extreme points is the central task, which is typical of direction sense questions that also require basic numerical calculation.

Given Data / Assumptions:

• The cat starts from an initial point.
• It moves 25 m north.
• It then takes a right turn from that north facing direction and moves 100 m, which means it moves east.
• Next, it turns towards the south and moves 25 m.
• Finally, it turns left from the south facing direction and moves 55 m, which means it moves east again.
• All motions are along straight segments with right angle turns.

Concept / Approach:
We use the coordinate framework. Let the starting point be (0, 0). We track each move as changes in x and y coordinates. After the north and south legs, we check whether the vertical displacement cancels. After the eastward legs, we sum the horizontal displacement. The net displacement forms a straight horizontal segment, and the distance between the initial and final positions is simply the absolute horizontal difference because the vertical component turns out to be zero.

Step-by-Step Solution:
Step 1: Start at (0, 0). After moving 25 m north, the cat is at (0, 25).Step 2: Facing north, a right turn means facing east. Moving 100 m east shifts the position to (100, 25).Step 3: The cat then turns south and moves 25 m, reducing the y coordinate back to 0 and arriving at (100, 0).Step 4: Now it faces south. A left turn from south means facing east. Moving 55 m east changes the position to (155, 0).Step 5: The starting point is (0, 0) and the final point is (155, 0). The vertical coordinate is the same in both, so there is no north south displacement and the net displacement is purely eastward.Step 6: Therefore, the straight line distance between the initial and final positions is 155 m.

Verification / Alternative check:
Track vertical and horizontal movements separately. Vertically, the cat goes 25 m north and later 25 m south, which exactly cancel. Horizontally, it goes 100 m east first and later 55 m east again, so total eastward movement is 155 m. With no westward leg at any stage, the final position must be 155 m east of the starting point. This logic matches the coordinate calculation and confirms our answer.

Why Other Options Are Wrong:
Option A (185 m) and Option C (190 m) are larger than the actual net eastward displacement and likely come from adding extra segments incorrectly. Option D (135 m) underestimates the distance, possibly by dropping one of the horizontal legs. Only option B correctly gives 155 m as the straight line separation between start and end points.

Common Pitfalls:
Many students forget that the north and south movements cancel exactly and incorrectly include them in the final distance calculation. Another error is misinterpreting the left turn from south, which must lead to east, not west. Drawing a simple diagram with all four legs marked clearly helps in seeing the final layout as a horizontal line between two points separated by 155 m.

Final Answer:
The distance between the initial and final positions of the cat is 155 m, so the correct option is “155 m”.