The line joining the points (2,1) and (5,8) is trisected by the points P and Q.If the point P lies on line 2x-y+K=0 ,find the value of K ?_____________solve in two to three steps if not solve long?

1 Answer
Oct 1, 2017

K=-8/3

Explanation:

Section formula :
If a point P(x,y) divides a line segment joining A(x_1,y_1)and B(x_2,y_2) in the ratio of m:n, i.e., (AP:PB=m:n),
then P(x,y)= ((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))
Given the line joining A(2,1) and B(5,8) is trisected by P and Q,
=> AP:PQ:QB=1:1:1,
=> AP:PB=1:2
=> P(x,y)=((1xx5+2xx2)/(1+2),(1xx8+2xx1)/(1+2))=(3,10/3)
Given P lies on the line 2x-y+K=0,
=> 2(3)-10/3+K=0
=> K=10/3-6=10/3-(18)/3=-8/3