Answer:
[tex]m_2 = -\frac{3}{4}[/tex] -- (a)
[tex]m_2 = -\frac{7}{3}[/tex] -- (b)
[tex]m_2 = -\frac{1}{4}[/tex] --- (c)
[tex]m_2 = -3[/tex] -- (d)
Step-by-step explanation:
Given
[tex]a.\ m = \frac{4}{3}[/tex]
[tex]b.\ m = \frac{3}{7}[/tex]
[tex]c.\ m = 4[/tex]
[tex]d.\ m = \frac{1}{3}[/tex]
Required
Determine the slope of a perpendicular line
In geometry, the condition for perpendicularity is:
[tex]m_2 = -\frac{1}{m}[/tex]
This formula will be applied in solving these questions.
[tex]a.\ m = \frac{4}{3}[/tex]
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute 4/3 for m
[tex]m_2 = -\frac{1}{4/3}[/tex]
Express as a proper division
[tex]m_2 = -1/ \frac{4}{3}[/tex]
Convert to *
[tex]m_2 = -1* \frac{3}{4}[/tex]
[tex]m_2 = -\frac{3}{4}[/tex]
[tex]b.\ m = \frac{3}{7}[/tex]
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute 3/7 for m
[tex]m_2 = -\frac{1}{3/7}[/tex]
Express as a proper division
[tex]m_2 = -1/ \frac{3}{7}[/tex]
Convert to *
[tex]m_2 = -1* \frac{7}{3}[/tex]
[tex]m_2 = -\frac{7}{3}[/tex]
[tex]c.\ m = 4[/tex]
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute 4 for m
[tex]m_2 = -\frac{1}{4}[/tex]
[tex]d.\ m = \frac{1}{3}[/tex]
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute 1/3 for m
[tex]m_2 = -\frac{1}{1/3}[/tex]
Express as a proper division
[tex]m_2 = -1/ \frac{1}{3}[/tex]
Convert to *
[tex]m_2 = -1* \frac{3}{1}[/tex]
[tex]m_2 = -\frac{3}{1}[/tex]
[tex]m_2 = -3[/tex]
