Which line is perpendicular to a line that has a slope of [tex]\frac{1}{2}[/tex]?
line AB
line CD
line FG
line HJ
Answer (2)
The problem requires finding a line perpendicular to a line with a slope of 2 1 .
Perpendicular lines have slopes that are negative reciprocals of each other.
The negative reciprocal of 2 1 is -2.
Therefore, a line with a slope of -2 is perpendicular to the given line.
Explanation
Problem Analysis We are given a line with a slope of 2 1 . We need to find a line that is perpendicular to this line.
Perpendicular Lines Two lines are perpendicular if the product of their slopes is -1. This means that if a line has a slope m , a line perpendicular to it has a slope of − m 1 , which is the negative reciprocal of m .
Calculate Negative Reciprocal The given line has a slope of 2 1 . The negative reciprocal of 2 1 is − 2 1 1 = − 2 . Therefore, a line perpendicular to the given line has a slope of -2.
Identify Perpendicular Line Now we need to check which of the given lines (AB, CD, FG, HJ) has a slope of -2. Since we don't have the slopes of these lines, we cannot determine which one is perpendicular to the given line. However, if one of the lines, say line CD, has a slope of -2, then that line is perpendicular to the line with slope 2 1 .
Final Answer Without knowing the slopes of lines AB, CD, FG, and HJ, we cannot definitively choose one. However, if line CD has a slope of -2, then line CD is perpendicular to the line with a slope of 2 1 .
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 known slope, architects use the principle of negative reciprocals to calculate the slope needed for the perpendicular wall. For example, if one wall has a slope of 2 1 , the perpendicular wall must have a slope of -2 to ensure they meet at a 90-degree angle, providing stability and proper alignment in the building's structure.
A line that is perpendicular to a line with a slope of 2 1 has a slope of -2. To find the correct line, we would need to check which of the provided lines has this slope. Without this information, we cannot definitively select a line from the options provided.
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