A line L passes through the point of intersection of the lines 3x + y - 10 = 0 and x - y - 2 = 0 . If the perpendicular distance of the line L from the point (5, 1) is exactly 2 5 units, which of the following represents the correct equation for line L?

Step-by-step solution

The point of intersection of the lines 3x + y - 10 = 0 and x - y - 2 = 0 is obtained by solving the two equations. Adding the equations gives 4x - 12 = 0 x = 3 . Substituting x = 3 into x - y - 2 = 0 gives y = 1 . Thus, the point of intersection is (3, 1) . Let the equation of the required line L passing through (3, 1) be y - 1 = m(x - 3) , which can be rewritten as mx - y - 3m + 1 = 0 . The perpendicular distance of line L from the point (5, 1) is given as 2 5 . Using the perpendicular distance formula: |m(5) - 1