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Determine whether the following points a...

Determine whether the following points are collinear or not:
`A(-4,4),K(-2,5/2),N(4,-2)`

Text Solution

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`A(-4,4),K(-2,5/2)` and `N(4,-2)`
Slope of line `AK=(5/2-4)/(-2-(-4))`
`=(5/2-4)/(-2+4)`
`=((5-8)/2):-2`
`=(-3)/2xx1/2`
`=-3/4`
Slope of line KN `=(-2-5/2)/(4-(-2))`
`=(((-4-5)/2))/6`
`=(-9)/2xx1/6=-3/4`
Slope of line `AK=` slope of line KN and K is the common point.
`:.` points A,K and N are collinear.
Points `A(-4,4),K(-2,5/2)` and `(4,-2)` are colllinear.
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