Aline segment has endpoints a(4, 8) and b(2, 10). the point m is the midpoint of ab. what is an equation of a line perpendicular to ab and passing through m?

I)

The Midpoint M of the line segment AB is found using the Midpoint formula:



ii)

the slope of the line through A and B is found by the slope formula:



iii)

the product of the slopes of 2 perpendicular lines is -1, so the slope of the line perpendicular to the line through A and B is -1/(-1)=1

iv) 

the equation of the line with slope 1, which contains point M(3, 9) is found by the slope point form equation of a line:

y-9=1(x-3)

y-9=x-3

y=x+6

y=x+6