Select the most precise and correct definition of perpendicular lines from among those that are given. Choose 1 answer: A Two lines are perpendicular if they have opposite slopes. B Two distinct lines are perpendicular if they are as far from being parallel as possible. C Two lines are perpendicular if they meet at one point and one of the angles at their point of intersection is a right angle.
The Correct Answer and Explanation is:
The correct answer is C: Two lines are perpendicular if they meet at one point and one of the angles at their point of intersection is a right angle.
Explanation:
Perpendicular lines are two lines that intersect at a right angle (90 degrees). The defining characteristic of perpendicular lines is that they form one or more angles of 90 degrees where they meet. This is a fundamental concept in geometry and is true regardless of whether the lines are vertical, horizontal, or slanted.
Why Option C is Correct:
- Option C correctly states that perpendicular lines meet at a point where one of the angles formed is a right angle (90 degrees). This is the precise definition of perpendicularity. The lines don’t necessarily need to have any specific slope properties; their defining feature is that they form a right angle when they intersect.
Why Other Options Are Incorrect:
- Option A suggests that two lines are perpendicular if they have opposite slopes. This is not entirely accurate. While it’s true that if two lines have slopes that are negative reciprocals of each other (e.g., the slope of one line is 2, and the slope of the other is -1/2), they will be perpendicular, this only applies to non-vertical lines. Vertical and horizontal lines are also perpendicular, but they don’t have slopes that are negative reciprocals.
- Option B defines perpendicular lines as being as far from parallel as possible, which is vague and incorrect. The concept of perpendicularity doesn’t rely on how “far” lines are from being parallel; rather, it depends on the angle at the point of intersection. Two lines can be very close to parallel but still meet at a right angle (if they are at a slight angle to each other).
Thus, Option C is the most precise and correct definition of perpendicular lines.
