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If each of the following represents the slope of a line (or line segment), give the slope a line that is perpendicular to it. (a) 4 3 m (b) 3 7 m ( c )4 m (d) 1 3

Sagot :

MrRoyal

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]

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