Case Study 2
Social Distance in Examination Hall
In an examination hall, students are seated at a distance of 2 m from each other, to maintain
the social distance due to CORONA virus pandemic. Let three students sit at points A, B
and C whose coordinates are (4,–3), (7,3) and (8,5) respectively. Based on the above
information, answer the following questions. The distance between A and C is 1
(a)
5 units
(b)
4 5 units
(c)
3 5 units
(d) None of these
Answers
Given : three students sit at points A, Band C whose coordinates are (4, -3), (7,3) and (8, 5) respectively.
If an invigilator at the point I, lying on the straight line joining Band C such that it divides the distance between them in the ratio of 1 : 2.
To Find : (i) The distance between A and C
Then coordinates of I
The mid-point of the line segment joining A and C is
The ratio in which B divides the line segment joining A and C
The points A, Band C lie on
Solution:
(i) The distance between A and C
A (4, -3), C (8, 5)
= √(8 - 4)² + (5 - (-3))²
= √(16 + 64)
= √80
= 4√5 units
B (7,3) and C (8, 5)
ratio of 1 : 2.
I = ( 1 * 8 + 2 * 7)/(1 + 3) , ( 1 * 5 + 2 * 3)/(1 + 2)
= (22/3 , 11/3)
B divides the line segment joining A and C k : 1
A (4, -3), C (8, 5)
=> 7 = ( k * 8 + 1 * 4)/( k + 1)
=> 7k + 7 = 8k + 4
=> k = 3
Hence 3 : 1
The points A, Band C lie on a straight line
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