To determine if the lines are parallel or perpendicular, we can examine their slopes. The slope of a line can be found using the formula:
slope = (change in y)/(change in x)
For line a, the coordinates are (-1,1) and (2,0). Using the slope formula, we can calculate the slope of line a.
slope_a = (0 - 1)/(2 - (-1)) = -1/3
For line b, the coordinates are (0,5) and (3,4). Let's calculate the slope of line b.
slope_b = (4 - 5)/(3 - 0) = -1/3
The slopes of line a and line b are the same (-1/3), which means they are parallel.
Now, let's check if any of the lines are perpendicular. For two lines to be perpendicular, their slopes must be negative reciprocals of each other.
To find the slope of line c, with coordinates (2,5) and (0,0), let's calculate it.
slope_c = (0 - 5)/(0 - 2) = 5/2
The slope of line c is 5/2, which is not the negative reciprocal of -1/3. Therefore, line c is not perpendicular to line a or line b.
In summary, line a and line b are parallel because they have the same slope (-1/3), while line c is neither parallel nor perpendicular to line a or line b