A person starts walking from point F towards the west. After walking for 27 m, he reaches point D. From point D, he takes a left turn and walks 20 m to reach point C. From point C, he turns right and walks 27 m to reach point B. From point B, he takes a right turn and walks 10 m to reach point A.

If point S lies exactly midway between points C and D, what is the distance and direction of point S from point A?

Question

A person starts walking from point F towards the west. After walking for 27 m, he reaches point D. From point D, he takes a left turn and walks 20 m to reach point C. From point C, he turns right and walks 27 m to reach point B. From point B, he takes a right turn and walks 10 m to reach point A.

If point S lies exactly midway between points C and D, what is the distance and direction of point S from point A?

Accepted Answer

**Solution:**

1. The person starts at point F and walks 27 m west to reach point D.

2. From D, he turns left (which is south) and walks 20 m to reach point C.

3. From C, he turns right (which is west) and walks 27 m to reach point B.

4. From B, he takes a right turn (which is north) and walks 10 m to reach point A.

5. Point S is exactly between points C and D, so it lies halfway on the line segment CD.

- Distance CD = 20 m, so CS = SD = 10 m.

6. Now, let's find the position of point S relative to point A:

- From A, move 10 m south to reach B (since A is 10 m north of B).

- From B, move 27 m east to reach C (since B is 27 m east of C, so C is 27 m west of B).

- From C, move 10 m north to reach S (since S is 10 m north of C).

7. Combining these movements from A to S:

- 10 m south (A to B)

- 27 m west (B to C)

- 10 m north (C to S)

Net vertical movement: 10 m south then 10 m north = 0 m (no vertical displacement)

Net horizontal movement: 27 m west

8. Therefore, point S is 27 m west of point A.

**Answer:** 27 m east is incorrect based on the above calculation. Let's re-examine the directions carefully.

**Re-examination:**

- The person starts at F and walks 27 m west to D.

- From D, he turns left (south) and walks 20 m to C.

- From C, he turns right (west) and walks 27 m to B.

- From B, he turns right (north) and walks 10 m to A.

Coordinates (assuming F at origin (0,0)):

- F: (0,0)

- D: 27 m west → (-27, 0)

- C: 20 m south from D → (-27, -20)

- B: 27 m west from C → (-54, -20)

- A: 10 m north from B → (-54, -10)

Point S is midpoint of C (-27, -20) and D (-27, 0):

- S_x = (-27 + -27)/2 = -27

- S_y = (-20 + 0)/2 = -10

So, S is at (-27, -10).

Distance and direction from A (-54, -10) to S (-27, -10):

- Horizontal distance = |-27 - (-54)| = 27 m

- Vertical distance = 0

Since S_x > A_x, S is 27 m east of A.

**Answer:** 27 m, east

This matches option (d).

**Answer:** (d) 27 m, east

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