The line L₂ passing through (3, -1) divides the line segment L₁ joining the points (-1, 2) and (3, 6) in the ratio 1 : 3 internally. The equation of line L₂ is:

Step-by-step solution

Let the given points be A(-1, 2) and B(3, 6) . Let P be the point that divides the line segment AB internally in the ratio 1 : 3 . Using the section formula, the coordinates of P are given by: x = 1(3) + 3(-1) 1 + 3 = 3 - 3 4 = 0 y = 1(6) + 3(2) 1 + 3 = 6 + 6 4 = 3 Thus, the coordinates of P are (0, 3) . The line L₂ passes through the points (3, -1) and (0, 3) . The slope of the line L₂ is: m = 3 - (-1) 0 - 3 = - 4 3 The equation of the line L₂ is: y - 3 = - 4 3 (x - 0) 3y - 9 = -4x 4x + 3y - 9 = 0 Answer: 4x + 3y