A line is passing through the points A2,3,B2,7 . The point where the line perpendicular to the line AB  and passing through 1,4  meets the line AB is

To get the required point, find the foot of the perpendicular from the point (1,4) on the line AB In the given points A(2,3),B(2,7),x-coordinates are equal. So that the equation of the  line AB is x=2 The foot of the perpendicular of a point (1,4) on the line x=2 is (2,4)