GATE CE 2021 Set 2 — Question 6
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.The distance of point Q to point O, in the same units, should be ________
Correct answer
(C) 5
Solution
Let the starting point O be at the origin .
At , . So, .
Equation of path from R: .
At , . So, .
Note: The phrasing 'point Q that is 8 units North of point P' can also be interpreted as Q having the same x-coordinate as P, i.e., . Let's check if (3, 4) is North-West of R(6, -1). From R to Q, (West) and (North). This is indeed a North-West direction. If , then distance .Distance .Therefore, the correct option is (C).
1.Travel 3 units East: New position is .
2.Travel 4 units South to arrive at P: .
3.Travel from P in North-East direction (slope = 1) to a point R that is 6 units East of O ():
Equation of path from P: .At , . So, .
4.Travel from R in North-West direction (slope = -1) to arrive at point Q that is 8 units North of P:
Point P is . 8 units North of P is the line .Equation of path from R: .
At , . So, .
Note: The phrasing 'point Q that is 8 units North of point P' can also be interpreted as Q having the same x-coordinate as P, i.e., . Let's check if (3, 4) is North-West of R(6, -1). From R to Q, (West) and (North). This is indeed a North-West direction. If , then distance .Distance .Therefore, the correct option is (C).
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