Final Answer:
The slopes of L10 and 10.18 are 2 and -2, respectively; as they neither have equal slopes (for parallelism) nor slopes whose product is -1 (for perpendicularity), these lines are neither parallel nor perpendicular. This understanding of slope relationships defines their geometric correlation in the coordinate plane.
Thus option c is correct.
Step-by-step explanation:
To determine if two lines are parallel or perpendicular, we can analyze their slopes. If two lines have the same slope, they are parallel. If the product of their slopes is -1, they are perpendicular. The equation of a line in slope-intercept form is y = mx + b, where 'm' is the slope.
For L10: If L10 has an equation y = 2x + 3, its slope (m) is 2.
For 10.18: If 10.18 has an equation y = -2x + 5, its slope (m) is -2.
The slopes of L10 and 10.18 are 2 and -2, respectively. Since their slopes are not the same (not equal to each other) and their product is not -1 (it's -4), these lines are neither parallel nor perpendicular.
This conclusion aligns with the fact that the slopes of parallel lines are equal, while the slopes of perpendicular lines have a product of -1. In this case, the slopes don’t meet either condition, confirming that L10 and 10.18 are neither parallel nor perpendicular. This understanding is crucial in geometry and trigonometry when studying the relationships between different lines in a coordinate plane. The importance lies in recognizing the characteristics that define parallelism and perpendicularity, aiding in the analysis of various geometric figures and their properties.
Therefore option c is correct.