Problem 40
Question
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I computed the slope of one line to be \(-\frac{3}{5}\) and the slope of a second line to be \(-\frac{5}{3},\) so the lines must be perpendicular.
Step-by-Step Solution
Verified Answer
The given statement does not make sense because the slopes of the two lines are not negative reciprocals of each other. Therefore, the lines are not perpendicular to each other.
1Step 1: Understanding the Concept about Slopes of Perpendicular Lines
The slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope \(m\), then the slope of the line perpendicular to it would be \(-1/m\).
2Step 2: Compare Given Slopes with This Concept
In this particular case, the slope of one line is given as \(-3/5\) and the other as \(-5/3\). To check if these are negative reciprocals, flip the slope of the first line and change the sign, essentially making the operation \(1/(-(-3/5)) = 5/3\). It gives \(5/3\), which is not equal to the slope of the second line. So, they are not negative reciprocals of each other.
Other exercises in this chapter
Problem 39
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