Asked 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)?

Answers

Answered by Steve
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.
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