The co-ordinates of the points on the line 2 x-y=5 which are the distance of 1 unit from the line 3 x+4 y=5 are

Step-by-step solution

Let (x₁, y₁ ) be the required point 2 x₁-y₁=5 Also, (x₁, y₁ ) is at the distance of 1 unit from line 3 x+4 y=5 array ll & 1= | 3 x₁+4 y₁-5 9+16 | & 5=3 x₁+4 y₁-5 & 3 x₁+4 y₁-5=5 or 3 x₁+4 y₁-5=-5 & 3 x₁+4 y₁=10 & or & 3 x₁+4 y₁=0 array Solving equations (i) and (ii), we get x₁= 30 11 and y₁= 5 11 Solving equation (i) and (iii), we get x₁= 20 11 and y₁= -15 11 ( 30 11 , 5 11 ) and ( 20 11 , -15 11 ) are the required points.