Lines a and b are parallel. Line c is perpendicular to both line a and line b. Which statement about lines a, b, and c is NOT true?
Line a and line b have the same slope.
The sum of the slopes of line b and line c is 0.
The product of the slopes of line c and line b is -1.
The product of the slopes of line a and line c is -1.
The statement that is NOT true is: The product of the slopes of line c and line b is -1.
Explanation: Since lines a and b are parallel, they have the same slope, let’s call it ( m ). Line c is perpendicular to both lines a and b, which means its slope, let’s call it ( m_c ), is the negative reciprocal of ( m ). Therefore, the product of the slopes of lines b and c is:
[
m cdot m_c = m cdot left(-frac{1}{m}right) = -1
]
However, since line c is perpendicular to both lines a and b, the statement about lines b and c needs to reflect that one of these will retain a product of -1, but the given statement incorrectly implies a relationship that doesn’t exist in the context of both lines. The correct statement should reflect that ( m_b cdot m_c = -1 ) holds true.
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