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 .
Recall that perpendicular lines have slopes that are negative reciprocals of each other.
Calculate the slope of the perpendicular line: m 2 = − m 1 1 = 5 6 .
Identify the line (JK, LM, NO, or PQ) that has a slope of 5 6 . The answer is the line with slope 5 6 .
Explanation
Understanding the problem The problem asks us to find a line that is perpendicular to a line with a given slope. We know that two lines are perpendicular if the product of their slopes is -1. Let's use this information to find the slope of the perpendicular line.
Setting up the equation Let m 1 be the slope of the given line, so m 1 = − 6 5 . Let m 2 be the slope of the line perpendicular to the given line. Then, the product of their slopes must be -1:
m 1 ⋅ m 2 = − 1
Solving for the perpendicular slope Now, we solve for m 2 :
m 2 = − m 1 1 = − ( − 6 5 ) 1 = 5 6
So, the slope of the perpendicular line is 5 6 .
Finding the line with the correct slope Now we need to determine which of the lines JK, LM, NO, or PQ has a slope of 5 6 . Without knowing the coordinates of the points J, K, L, M, N, O, P, and Q, we cannot determine the slopes of the lines. Therefore, we cannot determine which line is perpendicular to the given line. However, if we were given the slopes of the lines, we would choose the line with a slope of 5 6 .
Final Answer Since we found that the slope of the perpendicular line is 5 6 , we are looking for the line with this slope. Without additional information about the slopes of lines JK, LM, NO, and PQ, we cannot definitively choose one. Assuming one of the lines has a slope of 5 6 , that would be the correct answer.
Examples
Understanding perpendicular slopes is crucial in architecture and construction. When designing buildings, architects need to ensure that walls are perpendicular to the ground for stability. If a roof has a certain slope, engineers use the concept of perpendicular slopes to calculate the angle and direction of support beams, ensuring the structure's integrity.
The line perpendicular to a line with slope − 6 5 has a slope of 5 6 . To identify the correct line among JK, LM, NO, and PQ, you need to find out which one has that slope. Without that information, we can't pinpoint the exact line from the options provided.
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