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Section and Mid-Point Formula

Question
ICSEENIMA10018839
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The slope of a line joining  P ( 6, k )  and  Q (1- 3k, 3 ) is 12. Find

(i) k

(ii) Midpoint of  PQ, using the value of  ‘k’  found in  (i).

Solution

( i )  Slope of  PQ = 3 - k1 - 3 k - 6⇒ 12 = 3 - k- 3 k - 5⇒ - 3 k - 5 = 2 ( 3 - k )⇒ - 3 k - 5 = 6 - 2 k⇒ k =  - 11

 

( ii ) Substituting  k  in  p  and  Q,  we get

P ( 6, K ) = P ( 6, - 11 )   and 

Q ( 1 - 3 k, 3 )  =  Q ( 1 - 3 ( - 11 ), 3 )  =  Q ( 1 +  33, 3 )  =  Q ( 34, 3 )

∴ Midpoint of  PQ =  6 + 342, - 11 + 32                               =  402, - 82                               = ( 20, - 4 )

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