Convex combination of two scalars

Question

Let $a,b\in \mathbb{R} $ and let $t_1 ,t_2\in \mathbb{R} $ be such that $t_1,t_2\geq 0$ and $t_1+t_2=1$ then how is it possible that $a\leq t_1×a+t_2×b\leq b$

Answer 1

If $a \leq b$,

then $t_1a + t_2 b = t_1 a + (1- t_1)b \leq t_1b + (1- t_1)b = b$

Similarly, $t_1a + t_2 b = (1 - t_2)a + t_2b \geq (1 - t_2)a + t_2a = a$