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Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?
- a)8km, East
- b)12 km, North
- c)6km, East
- d)10km, North
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Fatima starts from point P, goes North for 3 km, and then East for 4km...
Understanding Fatima's Journey
Fatima's movements can be broken down into several segments to determine her final position relative to point P.
1. Initial Movement
- Fatima starts at point P.
- She travels North for 3 km, reaching a point that we can label as A.
- Then she moves East for 4 km, reaching point Q.
2. Position of Points
- After the movements, her coordinates are:
- Point P: (0, 0)
- Point A (3 km North of P): (0, 3)
- Point Q (4 km East of A): (4, 3)
3. Direction Towards Point P
- From point Q, she turns to face point P and travels 15 km South.
- Traveling South from Q (4, 3) means she goes down to:
- New position after moving South: (4, 3 - 15) = (4, -12)
4. Final Movement
- After reaching (4, -12), she then moves North for 6 km.
- This takes her to:
- New position: (4, -12 + 6) = (4, -6)
5. Distance from Point P
- To find the distance from point P (0, 0) to her final position (4, -6):
- The distance formula is:
sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 0)^2 + (-6 - 0)^2)
= sqrt(16 + 36)
= sqrt(52)
= 2*sqrt(13) ≈ 7.21 km
- However, breaking it down, she is 4 km East and 6 km South from point P, forming a right triangle.
6. Direction to Point P
- To return to point P, she should move 8 km, towards the Northwest direction.
Conclusion
Fatima is approximately 8 km from point P, and to reach point P, she needs to go East. Therefore, the correct answer is option A: 8 km, East.
Fatima's movements can be broken down into several segments to determine her final position relative to point P.
1. Initial Movement
- Fatima starts at point P.
- She travels North for 3 km, reaching a point that we can label as A.
- Then she moves East for 4 km, reaching point Q.
2. Position of Points
- After the movements, her coordinates are:
- Point P: (0, 0)
- Point A (3 km North of P): (0, 3)
- Point Q (4 km East of A): (4, 3)
3. Direction Towards Point P
- From point Q, she turns to face point P and travels 15 km South.
- Traveling South from Q (4, 3) means she goes down to:
- New position after moving South: (4, 3 - 15) = (4, -12)
4. Final Movement
- After reaching (4, -12), she then moves North for 6 km.
- This takes her to:
- New position: (4, -12 + 6) = (4, -6)
5. Distance from Point P
- To find the distance from point P (0, 0) to her final position (4, -6):
- The distance formula is:
sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 0)^2 + (-6 - 0)^2)
= sqrt(16 + 36)
= sqrt(52)
= 2*sqrt(13) ≈ 7.21 km
- However, breaking it down, she is 4 km East and 6 km South from point P, forming a right triangle.
6. Direction to Point P
- To return to point P, she should move 8 km, towards the Northwest direction.
Conclusion
Fatima is approximately 8 km from point P, and to reach point P, she needs to go East. Therefore, the correct answer is option A: 8 km, East.
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Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer?
Question Description
Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer?.
Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?a)8km, Eastb)12 km, Northc)6km, Eastd)10km, NorthCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
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