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)
The problem requires finding a line perpendicular to a line with a slope of − 3 1 .
Recall that the product of the slopes of two perpendicular lines is -1.
Calculate the slope of the perpendicular line: m 2 = − 1/ m 1 = − 1/ ( − 3 1 ) = 3 .
The line with a slope of 3 is perpendicular to the given line. Assuming line AB has a slope of 3, then the answer is: l in e A B .
Explanation
Problem Analysis We are given a line with a slope of − 3 1 . We need to find a line that is perpendicular to this line from the given options: line MN, line AB, line EF, and line JK.
Perpendicular Lines Condition Two lines are perpendicular if the product of their slopes is -1. Let m 1 be the slope of the given line and m 2 be the slope of the line perpendicular to it. Then, m 1 m 2 = − 1 .
Calculating the Slope We have m 1 = − 3 1 . We need to find m 2 such that m 1 m 2 = − 1 . So, we have
− 3 1 m 2 = − 1
Multiplying both sides by -3, we get
m 2 = 3
Finding the Perpendicular Line Therefore, the line perpendicular to the given line must have a slope of 3. Among the given options (line MN, line AB, line EF, line JK), the line with a slope of 3 is the line that is perpendicular to the given line.
Final Answer Without knowing the slopes of lines MN, AB, EF, and JK, we can only say that the line with a slope of 3 is perpendicular to the line with a slope of − 3 1 . Assuming that line AB has a slope of 3, then line AB is perpendicular to the line with a slope of − 3 1 .
Examples
Understanding perpendicular lines is crucial in architecture and construction. When designing buildings, ensuring walls are perpendicular to the ground is essential for stability. If a supporting beam has a slope, calculating the perpendicular slope helps in designing structures that distribute weight evenly and maintain structural integrity.
The line that is perpendicular to a line with a slope of − 3 1 must have a slope of 3. Assuming line AB is the one with a slope of 3, the answer is: l in e A B .
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