How do I evaluate and interpret these sets of vectors and their geometric descriptions?

$v=(5,2)$ and $w=(1,2)$.
a.

$v+cw $ represents a line in the plane that passes through the point $v=(5,2)$ (when $c=0$) and is parallel to the direction $w=(1,2)$.

b.

$av + bw$, $0\leq a \leq 1, 0 \leq b \leq1$, represents a parallelogram, whose sides are delimited by:

the line segment connecting the origin with $v$ (when $b=0$, $a$ ranging from $0$ to $1$, i.e, $a \in [0,1]$),
the line segment connecting the origin with $w$ (when $a=0$, $b \in [0,1]$),
the line segments connecting $v$ to $v+w$ (when $a=1$, $b\in [0,1]$),
the line segment connecting $w$ to $v+w$ (when $b=1$, $a\in [0,1]$).

Everything inside the parallelogram is also part of $av + bw$, (when $b\in (0,1)$, $a\in (0,1)$)

c.

$av+bw$, $0\leq a \leq 1$, $0\leq b \leq1$, $0 \leq a+b \leq 1$. This means that $b=1-a$, so that $av+(1-a)w = a(v-w)+w$

This represents a line that passes through $w$ ($a=0$) and is parallel to the vector $v-w$.

d.

$av+bw$, $a+b\leq 1, a \geq 0, b \geq 0$

This represents a triangle, delimited by:
the line segment connecting the origin with $v$ (when $b=0, a\in [0,1]$),
the line segment connecting the origin with $w$ (when $a=0, b\in [0,1]$),
the line segment connecting $v$ with $w$ (when $a+b =1$)

Everything inside the triangle is also part of $av + bw$, (when $a+b <1$)


I suggest making drawings to convince yourself of all this!