Question

Find the equation of a line which is perpendicular to 5x-2y-7=0 and passes through the mid point of the line segment joining (2, 4) and (4, 2).

Answer 1

Mid-point of the line segment joining (2, 4) and (4, 2) is [(2+4)/2,  (4+2)/2] i.e. (3, 3).

The slope of line 5x - 2y - 7 = 0 is 5/2 so, the slope of its perpendicular line is -2/5.
thus the equation must be 2x + 5y + λ = 0 
Also, this equation must be satisfied by the point (3, 3) 
so, 2(3) + 5(3) + λ = 0 
λ = -21
Thus the equation of the line is  2x + 5y - 21 = 0