Question

Given the points A(0, 0), B(e, f), C(0, e), and D(f, 0), determine if line segments AB and CD are parallel, perpendicular, or neither.

A) Parallel
B) Perpendicular
C) Neither
D) Insufficient information

Answer 1

The slopes of line segments AB and CD are negative reciprocals of each other, indicating that the lines are perpendicular. Hence, the answer is B) Perpendicular.

Step-by-step explanation:

To determine if line segments AB and CD are parallel, perpendicular, or neither, we need to compare their slopes. The slope of a line segment is the rate at which the 'y' value changes with respect to the 'x' value.

For line segment AB, the slope is (f - 0) / (e - 0), which simplifies to f/e. For line segment CD, the slope is (0 - e) / (f - 0), which simplifies to -e/f.

Since the slopes of AB and CD are negative reciprocals of each other (f/e and -e/f), the line segments are perpendicular.

Therefore, the correct answer is: B) Perpendicular.