Which line is perpendicular to a line that has a slope of $-\frac{5}{6}$?
line JK
line LM
line NO
line PQ
Answer (2)
The problem requires finding a line perpendicular to a line with slope − 6 5 .
The slope of a perpendicular line is the negative reciprocal of the given slope.
Calculate the negative reciprocal of − 6 5 , which is 5 6 .
The line with a slope of 5 6 is perpendicular to the given line. Without more information, we cannot determine which of the lines JK, LM, NO, or PQ has this slope, but if one of them does, that is the answer.
The slope of the perpendicular line is 5 6
Explanation
Analyze the problem The problem asks us to find a line that is perpendicular to a line with a given slope. We know that perpendicular lines have slopes that are negative reciprocals of each other. Let's find the negative reciprocal of the given slope.
Find the negative reciprocal The given slope is − 6 5 . To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of − 6 5 . The negative reciprocal is found by flipping the fraction and changing its sign.
Calculate the perpendicular slope The reciprocal of − 6 5 is − 5 6 . Now, we take the negative of this value: − ( − 5 6 ) = 5 6 . So, the slope of the perpendicular line is 5 6 .
Identify the perpendicular line Now we need to determine which of the lines JK, LM, NO, or PQ has a slope of 5 6 . Without additional information about the slopes of these lines, we cannot definitively choose one. However, if we assume that one of these lines has a slope of 5 6 , then that line would be perpendicular to the line with a slope of − 6 5 .
Examples
Understanding perpendicular slopes is crucial in architecture and construction. When designing buildings, ensuring walls are perpendicular to the ground or that different sections of a structure meet at right angles requires precise calculations of slopes. For example, if a roof has a slope of − 6 5 , engineers need to calculate the perpendicular slope of 5 6 to ensure proper water runoff and structural integrity.
The slope of a line that is perpendicular to a line with a slope of − 6 5 is 5 6 . To find which line (JK, LM, NO, or PQ) has this slope, more information about their slopes is needed. Without that information, we cannot definitively identify the perpendicular line.
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