Question

What is the shortest distance (in cm) for the red dot to reach the position x? The dot can travel only along the grid lines shown.

Hint:

In a grid-based path problem, break down the movement into simple horizontal and vertical steps. Carefully add up the length of each step. If there are multiple possible paths, you would need to calculate the length of each to find the shortest one. In a simple maze like this, there's often only one solution.

Answer 1

Step 1: Understanding the Concept:
The question asks for the shortest path between two points in a maze-like grid. Since movement is restricted to the grid lines, we need to find a valid path and calculate its total length. The length of each small grid segment is given as 1 cm.

Step 2: Detailed Explanation:
We need to trace the path from the starting point (the red dot at the arrow) to the end point (marked 'x'). Since there is only one possible path through the maze without crossing any walls, the shortest distance is simply the length of this unique path. We can calculate the total distance by summing the lengths of all the horizontal and vertical segments along the path.
Let's trace the path and sum the lengths of the segments:

Move Right: 1 cm
Move Down: 2 cm
Move Right: 1 cm
Move Up: 1 cm
Move Right: 2 cm
Move Down: 1 cm
Move Right: 1 cm
Move Down: 2 cm
Move Right: 2 cm
Move Up: 1 cm
Move Right: 1 cm
Move Up: 2 cm
Move Right: 1 cm
Let's sum the horizontal and vertical movements separately:
Total Horizontal Distance = 1 + 1 + 2 + 1 + 2 + 1 = 8 cm.
Total Vertical Distance = 2 + 1 + 1 + 2 + 1 + 2 = 9 cm. Wait, let's re-calculate the vertical path. Down: 2 + 1 + 2 = 5 cm. Up: 1 + 1 + 2 = 4 cm. Let me re-trace the path from the image again. A more careful trace:

Right by 1
Down by 2
Right by 1
Up by 1
Right by 2
Down by 1
Right by 1
Down by 2
Right by 2
Up by 1
Right by 1
Up by 2
Right by 1 to reach 'x'.
Let's sum the segments again: Horizontal segments (Right): \(1 + 1 + 2 + 1 + 2 + 1 = 8\) cm.
Vertical segments (Down and Up): \(2 (\downarrow) + 1 (\uparrow) + 1 (\downarrow) + 2 (\downarrow) + 1 (\uparrow) + 2 (\uparrow) = 9\) cm. There seems to be an error in my previous addition. Let's sum all segments directly: \(1+2+1+1+2+1+1+2+2+1+1+2+1 = 18\) cm.
Step 3: Final Answer:
The total length of the path is the sum of the lengths of all segments.
\[ \text{Total Distance} = \text{Sum of all horizontal and vertical segments} \] \[ \text{Total Distance} = 1 + 2 + 1 + 1 + 2 + 1 + 1 + 2 + 2 + 1 + 1 + 2 + 1 = 18 \text{ cm} \] The shortest distance for the red dot to reach position x is 18 cm.