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Find k, if PQ || RS and P(2,4), Q (3,6)...

Find k, if PQ `|| RS ` and P(2,4), Q (3,6), R (3,1), S(5,k).

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P(2,4), Q (3,6),R(3,1) and S(5,k) .
Line ` PQ ||` line RS
Parallel lines have equal slopes ,
` therefore ` slope of line PQ = slope of line RS
` therefore (6-4)/(3-2) = (k-1)/(5-1)`
` therefore (2)/(1) = (k-1)/(2)`
` therefore k - 1= 4 `
` therefore k = 4 + 1`
` therefore k = 5 `
k = 5
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