ANSWER
Parallel lines
EXPLANATION
To find the relationship between lines AB and CD, we have to find their slopes. If they have opposite reciprocal slopes, the lines are perpendicular; if they have the same slope and different y-intercept they are parallel; in any other case, they are neither parallel nor perpendicular.
The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]So, the slope of line AB is,
[tex]m_{AB}=\frac{5-(-1)}{1-(-2)}=\frac{5+1}{1+2}=\frac{6}{3}=2[/tex]And the slope of line CD is,
[tex]m_{CD}=\frac{5-1}{3-1}=\frac{4}{2}=2[/tex]Hence, since both lines have the same slope, AB and CD are parallel lines.
