Question

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

Answer 1

The students Rohini, Sandhya and Bina are seated in a line.

Explanation:

Given that in the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at $A(3,1)$ , $B(6,4)$ and $C(8,6)$

We need to determine the that the three students are seated in a line.

If the three students are seated in a line, then the line must satisfy one of the below three conditions.

The conditions are :

(1) $A B+B C=A C$

(2) $A B+A C=B C$ or

(3) $A C+B C=A B$

We shall find the length of AB, BC and CA using the distance formula, $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

$A B=\sqrt{(6-3)^{2}+(4-1)^{2}}$

     $=\sqrt{(3)^{2}+(3)^{2}}$

     $=\sqrt{9+9}$

     $=\sqrt{18}$

$AB=3\sqrt{2}$

$\mathrm{BC}=\sqrt{(8-6)^{2}+(6-4)^{2}}$

     $=\sqrt{(2)^{2}+(2)^{2}}$

     $=\sqrt{8}$

$BC=2 \sqrt{2}$      

$A C=\sqrt{(8-3)^{2}+(6-1)^{2}}$

      $=\sqrt{25+25}$

      $=\sqrt{50}$

$AC=5 \sqrt{2}$

Hence, it is obvious that $A B+B C=A C$

Thus, the three points A,B,C are collinear.

Thus, the three students are seated in a line.

Learn more:

(1) If A , B , C are collinear points such that A = ( 3 , 4 ) , B = ( 7 , 7 ) and AC = 10 , then C = ?

brainly.in/question/2248401

(2) If A. B and P are three collinear points, B lying between A and P, such that AB= 6cm,and AB * AP=BP^2.Prove that AB^2 +AP^2=3BP^2,and find the length of BP.

brainly.in/question/6749890

Answer 2

Answer:

hey mate,, here is your answer..

Step-by-step explanation:

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