How do use midpoint formula to find an endpoint?

1 Answer
Oct 29, 2014

If you know one endpoint (x_1,y_1)(x1,y1) and the midpoint (a,b)(a,b), but you do not know the other endpoint (x_2,y_2)(x2,y2), then by rewriting the midpoint formula:

{(a={x_1+x_2}/2 Rightarrow 2a=x_1+x_2 Rightarrow x_2=2a-x_1),(b={y_1+y_2}/2 Rightarrow 2b=y_1+y_2 Rightarrowy_2=2b-y_1):}

So, the unknown endpoint can be found by

(x_2,y_2)=(2a-x_1,2b-y_1)


I hope that this was helpful.