In Exercises 18-21, determine whether each pair of lines...

In Exercises $18-21$, determine whether each pair of lines through the points below is parallel, perpendicular, or neither.
$A(1,3) \quad B(6,0) \quad C(4,3) \quad D(1,-2) \quad E(-3,8) \quad F(-4,1) \quad G(-1,6) \quad H(4,-4)$
$\overrightarrow{A B}$ and $\overrightarrow{C D}$

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Key Concepts

Slope Calculation

Slope is a measure of the steepness and direction of a line in the coordinate plane. It is computed as the ratio of the difference in the y-coordinates to the difference in the x-coordinates between two points on the line. This concept is fundamental in determining how lines relate to each other in terms of direction, which is essential when classifying them as parallel or perpendicular.

Criteria for Parallel Lines

Two lines in the coordinate plane are parallel if they have identical slopes. Since the slopes represent the directions of the lines, if the slopes are equal, the lines will never intersect regardless of their positions, meaning they are parallel. This concept is applied by calculating slopes for both lines and comparing them.

Criteria for Perpendicular Lines

Two lines are perpendicular if their slopes are negative reciprocals of each other, which means that the product of their slopes equals -1. This relationship ensures that the lines intersect at a right angle (90 degrees). This condition is checked by calculating the slopes of both lines and multiplying them to see if the result is -1.

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