How to find one endpoint with the other end point and a point 1/3 away from it

Question

If you had one endpoint and a point 1/3 of the way away from that endpoint. How would you find the other endpoint?

Answer 1

In the above image, the one endpoint which you know about is $A$ and the point $\frac{1}{3}$ of total length away from $A$ is $C$. $C$ is hence one of the points of trisection. The other point of trisection is, say $D$.
Hence $AC=CD=DB$, $C$ is the mid-point of $\overline{AD}$, hence the co-ordinates of $D$, using Midpoint Formula would be $(2c-a,\ 2d-b)$.
And then since $D$ is the mid-point of $\overline{CB}$, the co-ordinates of $B$, again using Midpoint formula would be $(2[2c-a] - c,\ 2[2d-b] - d)$.
I hope that helps you.