Which line is perpendicular to a line that has a slope of $-\frac{5}{5}$?
line JK
line LM
line NO
line PQ
Answer (2)
Simplify the given slope: − 5 5 = − 1 .
Use the property that the product of the slopes of two perpendicular lines is -1.
Calculate the slope of the perpendicular line: m 2 = 1 .
Conclude that the line with a slope of 1 is perpendicular to the given line.
1
Explanation
Analyze the problem Let's first analyze the problem. We are given a line with a slope of − 5 5 and we need to find which of the given lines (JK, LM, NO, PQ) is perpendicular to it. Two lines are perpendicular if the product of their slopes is -1.
Simplify the slope First, simplify the given slope: − 5 5 = − 1
Define perpendicularity condition Now, let m 1 be the slope of the given line, so m 1 = − 1 . Let m 2 be the slope of a line perpendicular to the given line. Then the product of their slopes must be -1: m 1 m 2 = − 1
Substitute the given slope Substitute m 1 = − 1 into the equation: ( − 1 ) ⋅ m 2 = − 1
Solve for the perpendicular slope Solve for m 2 :
m 2 = − 1 − 1 = 1
Identify the perpendicular line Therefore, a line perpendicular to the given line must have a slope of 1. Among the given options, we need to identify the line with a slope of 1. Since we are not given the slopes of lines JK, LM, NO, and PQ, we can only say that the line with a slope of 1 is perpendicular to the given line. If line NO has a slope of 1, then line NO is perpendicular to the given line.
Final Answer Without additional information about the slopes of lines JK, LM, NO, and PQ, we cannot definitively determine which line is perpendicular. However, if we assume that line NO has a slope of 1, then line NO is perpendicular to the given line.
Examples
Understanding perpendicular slopes is crucial in architecture and construction. When designing buildings, architects use perpendicular lines to ensure walls are vertical and floors are horizontal, creating stable and functional structures. For example, the walls of a room are perpendicular to the floor, ensuring the room stands upright. This principle extends to more complex designs, where precise angles and slopes are essential for structural integrity and aesthetic appeal.
A line that is perpendicular to a line with a slope of − 5 5 (which simplifies to -1) must have a slope of 1. Without knowing the specific slopes of lines JK, LM, NO, and PQ, we cannot definitively identify the perpendicular line unless we confirm that one of these lines has a slope of 1. If line NO is found to have a slope of 1, then it is the correct choice.
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