The point on the line x+y=4 that lie at a unit distance from the line 4 x+3 y=10 is

Step-by-step solution

Let the point on the line x+y=4 be P(h, 4-h) . The distance d of point P(h, 4-h) from the line 4x+3y-10=0 is given by the formula d = |ax₁ + by₁ + c| a^2 + b^2 . Substituting the coordinates of P and the line equation: 1 = |4(h) + 3(4-h) - 10| 4^2 + 3^2 1 = |4h + 12 - 3h - 10| 16 + 9 1 = |h + 2| 5 |h + 2| = 5 This gives two cases: Case 1: h + 2 = 5 h = 3 . The point is (3, 4-3) = (3, 1) . Case 2: h + 2 = -5 h = -7 . The point is (-7, 4-(-7)) = (-7, 11) . Comparing with the given options, (-7, 11) is present. Answer