Question

line segment joining points A(2, 1) and 8(5, - 8)nisbtrisecred at the at points P and Q such that P is nearer to A. If P lies on the line given by 2x - y + k = 0, find the value of k​

Answer 1

Answer: k = 8

Step-by-step explanation:

P and Q are points of trisection and P is nearer  to A  

⟹ AP : PB = 1 : 2

So, P = ( mx2 + nx1 / m + n ; my2 + ny1 / m + n )

⟹ { 1 (5) + 2 (2) / 1 + 2 ; 1 (-8) + 2 (1) / 1 + 2 ) }

⟹ P( −3, 2 ) passes through 2x − y + k = 0

⟹ k = 8

Hope it helps :D