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Point P divides the line segment joining the points A ( 2,1 ) and B ( 5, -8 ) such that AP : AB = 1: 3. IF P lies 2x - y + k = 0 , then the value of k.

Since p divides AB in 1:3 ratio. therefore here m=1 and n=3. now,co ordinate of P = (mx2 + nx1 / m+n , my2 + ny1 / m+n ). =(5+6/4 , -8+3/4) =(11/4 , -5/4). therefore, P in X axis is 11/4 and and in Y axis is -5/3. as they satisfy2X -Y + K=0 =2×11/4 -(-5/4)+ K = 0 =11/2 + 5/3 + K = 0 = 33+10+6k=0 (by taking lcm) = 6k = -43 therfore k = -43/6.