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Find the distances between the following...

Find the distances between the following points:
`P(-6,-3),Q(-1,9)`

Text Solution

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`P(-6,-3)` and `Q(-1,9)`
Let `P(x_(1),y_(1))` and `Q(x_(2),y_(2))`
Here `x_(1)=-6,y_(1)=-3,x_(2)=-1` and `y_(2)=9`
By distance formula,
`d(P,Q)=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))`
`=sqrt([-1-(-6)]^(2)+[9-(-3)]^(2))`
`=sqrt((-1+6)^(2)+(12)^(2))`
`=sqrt(5^(2)+12^(2))`
`=sqrt(25+144)`
`=sqrt(169)=13`
`d(P,Q)=13`
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