Final answer:
After calculating the slopes, we find that lines a and b are parallel to each other as they have the same slope of 4. Line c is perpendicular to both lines a and b because its slope is the negative reciprocal of their slopes.
Step-by-step explanation:
To determine if lines a, b, and c are parallel or perpendicular, we first need to find the slopes of each line. The slope of a line can be found by using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points the line passes through.
For line a, which passes through (-1, -5) and (1, 3), the slope is (3 - (-5)) / (1 - (-1)) = 8/2 = 4. For line b, which passes through (-3, -7) and (1, 9), the slope is (9 - (-7)) / (1 - (-3)) = 16/4 = 4. For line c, which passes through (0, -2) and (4, -3), the slope is (-3 - (-2)) / (4 - 0) = -1/4.
Lines a and b have the same slope, which means they are parallel to each other. Line c has a slope that is the negative reciprocal of the slope of lines a and b, which means line c is perpendicular to lines a and b.