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In the seating arrangement of desks in a...

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

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
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