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)
To find a line perpendicular to one with a slope of − 3 1 , you need a line with a slope of 3 . Without the slopes of lines MN, AB, EF, or JK, we cannot determine which one is perpendicular. If one of these lines has a slope of 3 , that is the correct answer.
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The problem requires finding a line perpendicular to a line with a slope of − 3 1 .
Perpendicular lines have slopes that are negative reciprocals of each other.
Calculate the negative reciprocal of − 3 1 , which is 3.
The line with a slope of 3 is perpendicular to the given line. Since the slopes of lines MN, AB, EF, and JK are not provided, we cannot determine which line is perpendicular. If one of the lines has a slope of 3, that is the answer.
Explanation
Problem Analysis Let's analyze the problem. We are given a line with a slope of − 3 1 and we need to find which of the given lines (MN, AB, EF, JK) is perpendicular to it.
Key Concept: Perpendicular Lines The key concept here is that perpendicular lines have slopes that are negative reciprocals of each other. This means that if a line has a slope m , a line perpendicular to it will have a slope of − m 1 .
Calculating the Negative Reciprocal Now, let's calculate the negative reciprocal of the given slope, − 3 1 . The negative reciprocal is:
− ( − 3 1 ) 1 = 3
So, a line perpendicular to the given line must have a slope of 3.
Finding the Perpendicular Line Therefore, the line that is perpendicular to the line with slope − 3 1 must have a slope of 3. Without knowing the slopes of lines MN, AB, EF, and JK, we cannot definitively say which one is perpendicular. However, if one of these lines has a slope of 3, that would be the correct answer.
Examples
Understanding perpendicular slopes is crucial in many real-world applications, such as architecture and construction. For example, when building a house, the walls need to be perpendicular to the ground to ensure stability. If the ground has a slight slope, the walls need to be adjusted to maintain that perpendicularity. This is also important in road design, where roads need to intersect at certain angles for safety and efficiency.
