Question

5.
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, Band C whose coordinates are (4, -3), (7,3) and (8, 5) respectively.

Based on the above information, answer the following questions.

(i) The distance between A and C is
(a) √5 units (b) 4√5 units (c) 3√ ​​​​​5 units (d) none of these

(ii) 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. Then coordinates of I are
(a)(22/3,11/3) (b)(23/3,13/3) (c) (6,1) (d) (9,1)

(iii) The mid-point of the line segment joining A and C is
(a) (1.6) (b) (6.1) (c) (11/2,0) (d) none of these

(iv) The ratio in which B divides the line segment joining A and C is
(a) 2:1 (b) 3:1 (c) 1:2 (d) none of these

(v) The points A, Band C lie on
(a) a straight line (b) an equilateral triangle
(c) a scalene triangle (d) an isosceles triangle​

Answer 1

Answer:

1. 4√5
2. 22/3,11/3
3. 6,1
4. 3:1
5. scalene triangle

Hope it helped you

Answer 2

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

Learn more:

Draw a line segment of length 8 cm and divide it in the ratio 2:3 ...

brainly.in/question/13087562

find the ratio in which y axis divides the line segment joining the ...

brainly.in/question/11827274