Question

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.

A
$\sqrt{5}$
B
$4 \sqrt{5}$
C
$3 \sqrt{5}$
D None of these above



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Answer 1

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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