Question

Given points A(1, 5), B(-2, -1), C(1, 1),and D(3, 5), what type of lines are ABand CD?

Answer 1

Parallel lines

Step-by-step 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,

`m=(y_1-y_2)/(x_1-x_2)`

So, the slope of line AB is,

`m_(AB)=(5-(-1))/(1-(-2))=(5+1)/(1+2)=(6)/(3)=2`

And the slope of line CD is,

`m_(CD)=(5-1)/(3-1)=(4)/(2)=2`

Hence, since both lines have the same slope, AB and CD are parallel lines.