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In the following examples , can the segm...

In the following examples , can the segment joining the given points from a triangle ? If triangle is formed , state the type of the triangle considering sides of the triangle.
(ii) P(-2,-6) , Q (-4,-2) ,R(-5,0)

Text Solution

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`P(-2,-6),Q(-4,-2)` and `R(-5,0)`
By distance formula,
`PQ=sqrt([-4-(-2)]^(2)+[-2-(-6)]^(2))`
`=sqrt((-4+2)^(2)+(-2+6)^(2))`
`=sqrt((-2)^(2)+(4)^(2))`
`=sqrt(4+16)`
`=sqrt(20)`
`=sqrt(2xx2xx5)`
`=2sqrt(5)`
`QR=sqrt([-5-(-4)]^(2)+[0-(-2)]^(2))`
`=sqrt((-5+4)^(2)+(0+2)^(2))`
`=sqrt((-1)^(2)+(2)^(2))`
`=sqrt(1+4)`
`=sqrt(5)`
`PR=sqrt([-5-(-2)]^(2)+[0-(-6)]^(2))`
`=sqrt((-5+2)^(2)+(0+6)^(2))`
`=sqrt((-3)^(2)+(6)^(2))`
`=sqrt(9+36)`
`=sqrt(45)`
`=sqrt(3xx3xx5)`
`=3sqrt(5)`
`PQ+QR=2sqrt(5)+sqrt(5)`
`:.PQ+QR=3sqrt(5)`
`:.PQ+QR=PR`
`:.` points P,Q and R are collinear.
`:.DeltaPQR` is not formed.
The segment joining `P(-2,-6),Q(-4,-2)` and `R(-5,0)` does not form a triangle.
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