The element presentation of convex hull of the union of compact sets

Question

I want to show that the convex hull of the union of compact convex sets $k_{1}$ and $k_{2}$ in a locally convex topology linear space, consist of the points of the form $$ay_1+(1-a)y_2,\ \ \ \ \ y_1\in k_1, y_2\in k_2$$ where a is a number between 0 and 1. I can show that a point of the form above, belongs to the convex hull but the inverse is my problem.