A person is riding his bike on a straight road towards East from his college to city A and then to city B. At some point in between city A and city B, he suddenly realizes that there is not enough petrol for the journey. Also, there is no petrol pump on the road between these two cities. Based on the information, answer the questions
(i) The value of y is equal to
. a) 2 b) 3 c) 4 d) 5
(ii) The value of x is equal to
. a) 4 b) 5 c) 7 d) 8
(iii) If M is any point exactly between city A and city B, then coordinates of M are
. a) (5, 5) b) (4, 4) c)(6, 6) d) (3, 3)
(iv) The ratio in which A divides the line segment joining the points O and M is
. a) 1 : 2 b) 2 : 1 c) 3 : 2 d) 2 : 3
(v) If the person analyse the petrol at the point M (the mid point of AB), then what should be his decision?
a) Should he travel back to college
b) Should try his luck to move towards city B
c) Should be travel back to city A
d) None of these
Pls answer the question with explanation
Answers
Solution :-
→ College coordinates = (0,0)
→ City A coordinates = (2,y)
→ Distance between college and city A = 2√2 km .
so, using distance formula we get,
→ (0 - 2)² + (0 - y)² = (2√2)²
→ 4 + y² = 8
→ y² = 8 - 4
→ y = ± 2 .
since , person is moving in east direction , y will be positive .
therefore, y is equal to 2 . (Option a)
now,
→ City A = (2,2)
→ City B = (x,8)
→ AB = 6√2 km .
again, using distance formula we get,
→ (x - 2)² + (8 - 2)² = (6√2)²
→ (x - 2)² + 36 = 72
→ (x - 2)² = 72 - 36
→ (x - 2)² = (6)²
→ x - 2 = 6
→ x = 8 (Option d)
now, let coordinates of Mid points of city and city B is M(x,y) .
so,
→ x = (x1 + x2)/2 = (2 + 8)/2 = 5
→ y = (y1 + y2)/2 = (2 + 8)/2 = 5
therefore, Option (a) 5, 5 is correct answer .
now,
→ OA = 2√2 km
→ AM = (6√2)/2 = 3√2 km .
so,
→ OA : AM = 2√2 : 3√2 = 2 : 3 .
therefore, A divides the line segment joining the points O and M in the ratio (d) 2 : 3 .
since M is the mid - point of AB , in place of coming back to city A , now the person (b) Should try his luck to move towards city B .
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