i)
The Midpoint M of the line segment AB is found using the Midpoint formula:
[tex]M=( \frac{4+2}{2} , \frac{8+10}{2})=(3, 9)[/tex]
ii)
the slope of the line through A and B is found by the slope formula:
[tex]m= \frac{y_1-y_2}{x_2-x_1}= \frac{10-8}{2-4}= \frac{2}{-2}=-1 [/tex]
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
Answer: y=x+6
