If a line l passes through (k, 2 k),(3 k, 3 k) and (3,1), k 0 , then the distance from the origin to the line l is

Step-by-step solution

Given points A(k, 2 k), B(3 k, 3 k) and C(3,1) are collinear. array rlrl & & Slope of A B & = Slope of B C & 2 k-2 k 3 k-k & = 1-3 k 3-3 k & k 2 k & = 1-3 k 3-3 k 3-3 k=2(1-3 k) & 1 & =-3 k k=- 1 3 array Given points become A (- 1 3 ,- 2 3 ), B(-1,-1) and C(3,1) . Equation of line passing through B and C is array rlrl y+1 & = 1+1 3+1 (x+1) & & y+1 & = 2 4 (x+1) & 2(y+1) & =(x+1) & 2 y-x+1 & =0 array Now, the distance from (0,0) to the above line is d= |2(0)-0+1| 2^2+1^2 = 1 4+1 = 1 5 Alternate Solution Equation of