How to paste a line so that endpoints line up
 

In design modeler, I want to copy a section of a curve, starting at the red circle, and paste it to make a continuous curve at the purple circle. I can copy the segments together as one cuve, but it seems I cannot get the pasted curve to match at the endpoint to form a continuous curve. How do I make sure they points overlap exactly? Please tell step-by-step to make this work.

Thanks

https://i.imgur.com/LnOBAeP.png