Slope of a line L  is 1. The points on the line L at a distance of 2 units from the point 32,32 which lies on the line L are

The inclination of the line L is θ=tan−1⁡(1)=π4 The coordinates of a point on the line L at a distance of r units from x1,y1 are x=x1±rcos⁡θ and y=y1±rsin⁡θ, here θ is inclination of the line θx=x1±rcos⁡θ and y=y1±rsin⁡θ, here θ is inclination of the line θHence the required coordinates are x=x1±rcosθ=32±212=32±2=42,22and y=y1±rsinθ=32±212=32±2=42,22 Therefore, the required points are (42,42)=(22,22)