In the rectangular coordinate plane, the graphs of $f$, $g$, and $h$ linear functions defined on the closed interval $[0,1]$ are given in the figure.
Let $a$ and $b$ be real numbers in the open interval $(0,1)$ and
$$f(1) = g(1)$$
$$f(a) = g(b) = h(b)$$
equalities are satisfied.
Accordingly, which of the following orderings is correct?
A) $f(a) < h(a) < g(a)$
B) $g(a) < f(a) < h(a)$
C) $g(a) < h(a) < f(a)$
D) $h(a) < f(a) < g(a)$
E) $h(a) < g(a) < f(a)$