Question

let line 1 with slope m1 and line 2 with slope m2 be two non - vertical perpendicular lines. which of the following statements is not true? choose the incorrect statement. a. the value of m1 does not equal the value of m2. b. if m1 = a/b, then m2=-b/a. c. the product m1m2 is equal to - 1. d. it is possible for the value of m1 to be zero.

Explanation:

Step1: Recall slope - perpendicular line property

For two non - vertical perpendicular lines with slopes $m_1$ and $m_2$, the product $m_1m_2=-1$. If $m_1 = 0$, the line is horizontal and there is no non - vertical perpendicular line (a vertical line has an undefined slope). So, the slope of a non - vertical perpendicular line to a non - vertical line cannot be zero.

Step2: Analyze option A

The slopes of two non - vertical perpendicular lines are different in general, so $m_1
eq m_2$ is a valid statement.

Step3: Analyze option B

If $m_1=\frac{a}{b}$, then from $m_1m_2=-1$, we can solve for $m_2$: $m_2 =-\frac{b}{a}$ (assuming $a
eq0$ and $b
eq0$), so this is a valid statement.

Step4: Analyze option C

For two non - vertical perpendicular lines, $m_1m_2=-1$ is a fundamental property, so this is a valid statement.

Step5: Analyze option D

As mentioned before, if $m_1 = 0$, the line is horizontal and there is no non - vertical perpendicular line. So, it is not possible for the slope of a non - vertical perpendicular line to be zero. This statement is incorrect.

Answer:

D. It is possible for the value of $m_1$ to be zero