Question

Given the points A(0, 0), B(1, f), C(0, e), and D(f, 0), determine if line segments AB and CD are:

A. Parallel
B. Perpendicular
C. Neither

Answer 1

By calculating the slopes of line segments AB and CD, we determine that they are neither parallel nor perpendicular unless additional conditions are met that make their slopes negative reciprocals of each other.

Step-by-step explanation:

To determine if line segments AB and CD are parallel or perpendicular, we need to compare their slopes. Point A (0, 0) and point B (1, f) create line segment AB. The slope of AB can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) is point A and (x2, y2) is point B. This gives us a slope of (f - 0) / (1 - 0), which simplifies to f.

Now, for line segment CD, we have point C (0, e) and point D (f, 0). Similarly, the slope of CD is (0 - e) / (f - 0), simplifying to -e/f. Two lines are perpendicular if their slopes are negative reciprocals of each other. In this case, we can see that the slope of AB, f, is not the negative reciprocal of the slope of CD, -e/f, as their product is not -1.

Therefore, line segments AB and CD are neither parallel nor perpendicular unless further specific conditions are given that make f and e/f negative reciprocals.