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

Given that the  line  is perpendicular to 5x-2y-7=0 .

Also it  passes through the midpoint of the line segment joining (2, 4) and (4, 2).

Find the midpoint using midpoint formula

Mid point = (6/2, 6/2) = (3,3)

Since line is perpendicular to 5x-2y -7=0 the line would have equation of the form 2x+5y =k

Use the fact that it passes through (3,3)

2(3)+5(3) = k Or k = 21

So required line equation is 2x+5y = 21