Question

How do use midpoint formula to find an endpoint?

Answer 1

If you know one endpoint `(x_1,y_1)` and the midpoint `(a,b)`, but you do not know the other endpoint `(x_2,y_2)`, 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)`

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I hope that this was helpful.