Answer
Line $a$ and line $b$ are parallel. No perpendicular lines.
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $a$ and $b$ are same, line $a$ and line $b$ are parallel.
Work Step by Step
For line $a$, slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{13-10}{4-2}=\frac{3}{2}$
For line $b$, $m=\frac{12-9}{6-4}=\frac{3}{2}$
For line $c$, $m=\frac{9-10}{4-2}=\frac{-1}{2}$
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $a$ and $b$ are same, line $a$ and line $b$ are parallel.
