Which line is perpendicular to a line that has a slope of $-\frac{1}{3}$?
A. line MN
B. line $AB$
C. line EF
D. line JK
Answer (1)
The problem requires finding a line perpendicular to a line with a slope of − 3 1 .
The negative reciprocal of − 3 1 is calculated by flipping the fraction and changing the sign: − 1/ ( − 3 1 ) = 3 .
A line with a slope of 3 is perpendicular to the given line.
Assuming line EF has a slope of 3, then line EF is the perpendicular line. EF
Explanation
Understanding Perpendicular Slopes Let's find the slope of a line that is perpendicular to a line with a slope of − 3 1 . Remember that perpendicular lines have slopes that are negative reciprocals of each other. This means we need to flip the fraction and change its sign.
Calculating the Negative Reciprocal To find the negative reciprocal of − 3 1 , we first take the reciprocal, which is − 3 . Then, we take the negative of that, which is − ( − 3 ) = 3 . So, the slope of the perpendicular line is 3.
Identifying the Perpendicular Line Now we need to determine which of the given lines (MN, AB, EF, JK) has a slope of 3. Since the problem doesn't provide the slopes of these lines, we'll assume that one of them has a slope of 3. Without additional information, we can't definitively say which line is perpendicular. However, if line EF has a slope of 3, then line EF is perpendicular to the line with a slope of − 3 1 .
Conclusion Therefore, the line perpendicular to a line with a slope of − 3 1 has a slope of 3. Assuming line EF has a slope of 3, then line EF is the perpendicular line.
Examples
In architecture, ensuring walls are perpendicular is crucial for structural integrity. If a design requires a wall to be perpendicular to another that has a slope of − 3 1 (perhaps due to the landscape), architects would calculate the necessary slope for the new wall to be 3. This ensures the walls meet at a perfect right angle, providing stability and safety to the building.
