A toy robot starts at point P and moves 5 m towards the East to point Q. At Q it turns left and moves 12 m to point R. At R it turns left and moves 9 m to point S. At S it turns left and moves 7 m to point T. Match List-I with List-II.
| List-I (Position) | List-II (Direction) | ||
|---|---|---|---|
| (A) | R with respect to P | (I) | South-West |
| (B) | S with respect to P | (II) | North-East |
| (C) | Q with respect to S | (III) | South-East |
| (D) | T with respect to R | (IV) | North-West |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
Each left turn moves the facing direction one step anticlockwise: East → North → West → South. Take P as the origin and write every point as (metres east, metres north).
Q: 5 m East → (5, 0)
R: left turn, 12 m North → (5, 12)
S: left turn, 9 m West → (\(5-9=-4\), 12), that is 4 m west and 12 m north of P
T: left turn, 7 m South → (\(-4\), \(12-7=5\))
(A) R from P: 5 east, 12 north → North-East → (II)
(B) S from P: 4 west, 12 north → North-West → (IV)
(C) Q from S: \(5-(-4)=9\) east, \(0-12=-12\), that is 12 south → South-East → (III)
(D) T from R: \(-4-5=-9\), that is 9 west, \(5-12=-7\), that is 7 south → South-West → (I)
So the matching is (A)-(II), (B)-(IV), (C)-(III), (D)-(I).
