Final answer:
The slope of a perpendicular line is the negative reciprocal of the original line's slope. If the original line has a slope 'm', the perpendicular line will have a slope '-1/m'. This rule does not apply to horizontal or vertical lines.The correct option is:
A) The slope of a perpendicular line is the negative reciprocal of the original line's slope.
Step-by-step explanation:
To find the slope of a perpendicular line, option A is correct: The slope of a perpendicular line is the negative reciprocal of the original line's slope. If a line has a positive slope, the perpendicular line will have a negative slope, and vice versa. For example, if the original line has a slope of 2 (which is positive), the perpendicular line will have a slope of -1/2, which is the negative reciprocal. Similarly, if the original line has a slope of -3/4, the perpendicular line will have a slope of 4/3.
An easy way to remember this is that the slopes of perpendicular lines are opposite in sign and reciprocal in magnitude. Think of a line with a positive slope: it 'rises' as it 'runs' to the right. A line perpendicular to it will 'fall' as it 'runs' to the right, reflecting the opposite type of slope.
It's important to note that this rule does not apply if the original line has a horizontal or vertical orientation. A horizontal line has a slope of zero, and any line perpendicular to it will have an undefined slope (vertical line), while a vertical line also has an undefined slope, and any line perpendicular to it will have a slope of zero (horizontal line).The correct option is:
A) The slope of a perpendicular line is the negative reciprocal of the original line's slope.