Question

A line 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?

Answer 1

I)

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

$M=( \frac{4+2}{2} , \frac{8+10}{2})=(3, 9)$

ii)

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

$m= \frac{y_1-y_2}{x_2-x_1}= \frac{10-8}{2-4}= \frac{2}{-2}=-1$

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