More math linear equation help?
posted by Lily .
I'm looking at this graph where I see a line AB with the points (2,2) and (2,8). Then I have to do the following:
a) Find the length of AB
b) Find the midpoint of AB
c) Write an equation for the line going through AB
I don't understand how to do part a and c, so could somebody help me there? And would the midpoint of AB be (0,4)?

Think of the two points as lying on the ends of the diagonal of a rectangle (or, the hypotenuse of a right triangle).
So, the length d^2 = 4^2+6^2 = 52
d = 2√13
The midpoint is the average of the endpoints: (0,5)
The slope of the line is constant, and between any two points, is ∆y/∆x
We have two points, so the slope is 4/6 = 2/3
Now we have a slope (2/3) and a point (2,2). For any other point (x,y) on the line, the slope remains constant, so
(y2)/(x+2) = 2/3
y2 = 2/3 (x+2)
You can massage that into any other form you need.