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P is 6 km west from point Q. Point R is 4 km north to point Q. S is 12 km south from point R. Now point S in which direction and how far from point P?
- a)10 km, South-East
- b)16 km, North-East
- c)10 km, South-West
- d)12 km, North-West
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
P is 6 km west from point Q. Point R is 4 km north to point Q. S is 12...
As per the given information;
Distance between S and P = √(PQ2 + QS2)
SP = √(62 + 82)
SP = √(36 + 64)
SP = √100
SP = 10 km
Hence, S is 10 km in South-East with respect to P.
SP = √(62 + 82)
SP = √(36 + 64)
SP = √100
SP = 10 km
Hence, S is 10 km in South-East with respect to P.
Most Upvoted Answer
P is 6 km west from point Q. Point R is 4 km north to point Q. S is 12...
Understanding the Positions of Points
To determine the direction and distance of point S from point P, we need to analyze the positions of the points based on the given information.
Step 1: Locate the Points on a Coordinate System
- Point Q: Consider this as the origin (0, 0).
- Point P: Since P is 6 km west of Q, its coordinates are (-6, 0).
- Point R: R is 4 km north of Q, placing it at (0, 4).
- Point S: S is 12 km south of R, which moves it down to (0, 4 - 12) = (0, -8).
Step 2: Calculate the Distance and Direction from P to S
- Coordinates of P: (-6, 0)
- Coordinates of S: (0, -8)
Step 3: Distance Calculation
To find the distance between points P and S, we can use the distance formula:
- Distance = √[(x2 - x1)² + (y2 - y1)²]
- Distance = √[(0 - (-6))² + (-8 - 0)²]
- Distance = √[6² + (-8)²] = √[36 + 64] = √100 = 10 km
Step 4: Determine the Direction
- From P (-6, 0) to S (0, -8), S is located in the South-East direction relative to P.
Final Conclusion
Therefore, point S is 10 km away from point P, and the direction is South-East. Thus, the correct answer is option A) 10 km, South-East.
To determine the direction and distance of point S from point P, we need to analyze the positions of the points based on the given information.
Step 1: Locate the Points on a Coordinate System
- Point Q: Consider this as the origin (0, 0).
- Point P: Since P is 6 km west of Q, its coordinates are (-6, 0).
- Point R: R is 4 km north of Q, placing it at (0, 4).
- Point S: S is 12 km south of R, which moves it down to (0, 4 - 12) = (0, -8).
Step 2: Calculate the Distance and Direction from P to S
- Coordinates of P: (-6, 0)
- Coordinates of S: (0, -8)
Step 3: Distance Calculation
To find the distance between points P and S, we can use the distance formula:
- Distance = √[(x2 - x1)² + (y2 - y1)²]
- Distance = √[(0 - (-6))² + (-8 - 0)²]
- Distance = √[6² + (-8)²] = √[36 + 64] = √100 = 10 km
Step 4: Determine the Direction
- From P (-6, 0) to S (0, -8), S is located in the South-East direction relative to P.
Final Conclusion
Therefore, point S is 10 km away from point P, and the direction is South-East. Thus, the correct answer is option A) 10 km, South-East.
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P is 6 km west from point Q. Point R is 4 km north to point Q. S is 12 km south from point R. Now point S in which direction and how far from point P?a)10 km, South-Eastb)16 km, North-Eastc)10 km, South-Westd)12 km, North-WestCorrect answer is option 'A'. Can you explain this answer?
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