Which line is perpendicular to a line that has a slope of $-\frac{1}{3}$?
line MN
line $AB$
line EF
line JK
Answer (2)
The problem requires finding a line perpendicular to a line with a slope of − 3 1 .
The negative reciprocal of − 3 1 is calculated as 3.
A line perpendicular to the given line must have a slope of 3.
Without knowing the slopes of lines MN, AB, EF, and JK, we cannot determine which line is perpendicular, but we know its slope must be 3 .
Explanation
Analyze the problem The problem asks us to identify which of the given lines is perpendicular to a line with a slope of − 3 1 . We know that two lines are perpendicular if the product of their slopes is -1. Therefore, we need to find the negative reciprocal of the given slope.
Find the negative reciprocal To find the negative reciprocal of a number, we first find its reciprocal and then change its sign. The reciprocal of − 3 1 is − 3 . Then, we take the negative of − 3 , which is − ( − 3 ) = 3 .
Determine the slope of the perpendicular line Therefore, a line perpendicular to a line with a slope of − 3 1 must have a slope of 3. Among the given options (line MN, line AB, line EF, line JK), we need to identify the line with a slope of 3. Since the slopes of the lines MN, AB, EF, and JK are not explicitly given, we cannot definitively determine which line has a slope of 3. However, we know that the perpendicular line must have a slope of 3.
State the condition for perpendicularity Without additional information about the slopes of lines MN, AB, EF, and JK, we cannot determine which of these lines is perpendicular to the line with a slope of − 3 1 . However, we know that the perpendicular line must have a slope of 3.
Examples
In architecture, ensuring walls are perpendicular is crucial for structural integrity. If a design requires a wall to be perpendicular to a wall with a slope of − 3 1 , the new wall must be built with a slope of 3 to ensure it stands correctly and supports the structure as intended. This principle applies to various construction and design scenarios where perpendicularity is essential.
A line perpendicular to a line with a slope of − 3 1 must have a slope of 3. Without knowing the slopes of the given lines, we cannot determine which specific line is perpendicular. The correct answer must be a line with a slope of 3.
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