Home
Class 10
MATHS
Figure  shows the arrangement of desks i...

Figure  shows the arrangement of desks in a classroom Ashima, Bharti and Camella are seated at A(3, 1), B(6, 4) and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer.

(ii) Which mathematical concept is used in the above problem ?
(iii) What is its value ?

Text Solution

Verified by Experts

Using the distance formula we have
`AB=sqrt((6-3)^2+(4-1)^2)=sqrt(9+9)=sqrt(18)=3sqrt2`
`BC=sqrt((8-6)^2+(6-4)^2)=sqrt(4+4)=sqrt(8)=2sqrt2`
`AC=sqrt((8-3)^2+(6-1)^2)=sqrt(25+25)=sqrt(50)=5sqrt5`
Since , `AB+BC=3sqrt2+2sqrt2=5sqrt2=AC`
We can say that `A,B,C` are `"collinear"` , so they are seated in a line
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    NCERT|Exercise EXERCISE 7.3|5 Videos

  • COORDINATE GEOMETRY

    NCERT|Exercise EXERCISE 7.2|10 Videos

  • CONSTRUCTIONS

    NCERT|Exercise EXERCISE 11.2|7 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NCERT|Exercise EXERCISE 8.3|7 Videos

Similar Questions

Explore conceptually related problems

The given figure, shows the arrangement of desks in a classroom. Ashima, Bharti and Camell are seated at A (3,1), B(6,4) and C(8,6) respectively. Find the distance between Bharti and Camella,

The given figure, shows the arrangement of desks in a classroom. Ashima, Bharti and Camell are seated at A (3,1), B(6,4) and C(8,6) respectively. Find the distance between Ashima and Bharti.

In the seating arrangement of desks in a classoom three studens Rohini,Sandhya and Bina are seated at A(3,1),B(6,4) and C(8,6). Do you think they are seated in al line?

The given figure, shows the arrangement of desks in a classroom. Ashima, Bharti and Camell are seated at A (3,1), B(6,4) and C(8,6) respectively. At how much distance Ashima is seated from Camella ?

The given figure, shows the arrangement of desks in a classroom. Ashima, Bharti and Camell are seated at A (3,1), B(6,4) and C(8,6) respectively. Write the formula for mid- points of two points :

The given figure, shows the arrangement of desks in a classroom. Ashima, Bharti and Camell are seated at A (3,1), B(6,4) and C(8,6) respectively. Write the formula for distance between : (x_(1),y_(1)) and (x_(2),y_(2))

The given figure shows the arrangement of charis in a classroom. Dinesh, Mohan and Sohan are seated at A (1,1) B (-2,7) and C (3,-3) respectively. Name the quadrant in which Dinesh is seated.

The given figure shows the arrangement of charis in a classroom. Dinesh, Mohan and Sohan are seated at A (1,1) B (-2,7) and C (3,-3) respectively. Find the distance between Dinesh and Sohan.

The given figure shows the arrangement of charis in a classroom. Dinesh, Mohan and Sohan are seated at A (1,1) B (-2,7) and C (3,-3) respectively. Find the distance between Dinesh and Mohan.

The given figure shows the arrangement of charis in a classroom. Dinesh, Mohan and Sohan are seated at A (1,1) B (-2,7) and C (3,-3) respectively. Name the quadrant in which Sohan is seated.