Question

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)?

Answer 1

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

(y-2)/(x+2) = 2/3
y-2 = 2/3 (x+2)

You can massage that into any other form you need.