A line L₁ passes through the points (h, k),(1,2) and (-3,4) . The points (4,3) and (h, k) lie on the line L₂ . Given L₁ L₂ then (k-h) equals to

Step-by-step solution

The line L₁ passes through (1, 2) and (-3, 4) . The slope of L₁ , denoted by m₁ , is calculated as m₁ = 4 - 2 -3 - 1 = 2 -4 = - 1 2 . Since L₁ also passes through (h, k) , the slope between (h, k) and (1, 2) must be equal to m₁ . Thus, k - 2 h - 1 = - 1 2 , which implies 2(k - 2) = -(h - 1) , or 2k - 4 = -h + 1 , leading to h + 2k = 5 . The line L₂ passes through (4, 3) and (h, k) . The slope of L₂ , denoted by m₂ , is m₂ = k - 3 h - 4 . Given L₁ L₂ , the product of their slopes is -1 , so m₁ m₂ = -1 . Substituting