Tara starts from Point C and walks 23 m towards the south. She takes a left…
2025
Tara starts from Point C and walks 23 m towards the south. She takes a left turn, walks 10 m and then takes a left turn, walks 17 m, reaches Point D and stops. Bruce starts from Point P, which is 15 m from the east of Point D. He walks 6 m towards the north, takes a left turn, walks 16 m and stops at Point Q. What is the shortest distance between Point Q and Point C? (All turns are 90-degree turns only)
Answer: D. 9 m — Concept: A direction-sense path is solved by fixing one origin and two perpendicular axes, then writing every leg as a change in exactly one coordinate — take…
- A.
7 m
- B.
11 m
- C.
16 m
- D.
9 m
Show answer & explanation
Correct answer: D
Concept: A direction-sense path is solved by fixing one origin and two perpendicular axes, then writing every leg as a change in exactly one coordinate — take east as the positive x-direction and north as the positive y-direction.
A left turn rotates the walker 90 degrees anticlockwise, so the facing cycles from north to west to south to east and back to north. Once both endpoints are written as coordinates, the shortest distance between them is the straight line joining them.
Application: track each leg of the two walks as a change in one coordinate.
Place Point C at the origin (0, 0), with east as +x and north as +y.
Tara walks 23 m south from C, reaching (0, -23), and is now facing south.
Facing south, her left turn points her east; walking 10 m east takes her to (10, -23).
Facing east, her next left turn points her north; walking 17 m north takes her to (10, -23 + 17) = (10, -6), which is Point D.
Point P lies 15 m east of D, so P is at (10 + 15, -6) = (25, -6).
Bruce walks 6 m north from P, reaching (25, -6 + 6) = (25, 0), and is now facing north.
Facing north, his left turn points him west; walking 16 m west takes him to (25 - 16, 0) = (9, 0), which is Point Q.
C is at (0, 0) and Q is at (9, 0), so the east-west change is 9 and the north-south change is 0. The straight-line distance is the square root of the sum of the squares of these two changes.
√(92 + 02) = √81 = 9
Cross-check: Tara ends 10 m east and 6 m south of C, while Bruce ends 16 m west and 6 m north of P. Bruce’s 6 m northward leg exactly cancels Tara’s 6 m southward net displacement, so Q sits on the same east-west line as C and no north-south gap survives.
The whole east-west account is therefore 10 m east from Tara, plus 15 m east from D to P, minus 16 m west from Bruce, giving 9 m east. With the north-south gap zero, the straight-line distance equals that east-west gap.
The shortest distance between Point Q and Point C is 9 m.