Question

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

Answer 1

`m_2 = -(3)/(4)` -- (a)

`m_2 = -(7)/(3)` -- (b)

`m_2 = -(1)/(4)` --- (c)

`m_2 = -3` -- (d)

Explanation:

Given

`a.\ m = (4)/(3)`

`b.\ m = (3)/(7)`

`c.\ m = 4`

`d.\ m = (1)/(3)`

Required

Determine the slope of a perpendicular line

In geometry, the condition for perpendicularity is:

`m_2 = -(1)/(m)`

This formula will be applied in solving these questions.

`a.\ m = (4)/(3)`

`m_2 = -(1)/(m)`

Substitute 4/3 for m

`m_2 = -(1)/(4/3)`

Express as a proper division

`m_2 = -1/ (4)/(3)`

Convert to *

`m_2 = -1* (3)/(4)`

`m_2 = -(3)/(4)`

`b.\ m = (3)/(7)`

`m_2 = -(1)/(m)`

Substitute 3/7 for m

`m_2 = -(1)/(3/7)`

Express as a proper division

`m_2 = -1/ (3)/(7)`

Convert to *

`m_2 = -1* (7)/(3)`

`m_2 = -(7)/(3)`

`c.\ m = 4`

`m_2 = -(1)/(m)`

Substitute 4 for m

`m_2 = -(1)/(4)`

`d.\ m = (1)/(3)`

`m_2 = -(1)/(m)`

Substitute 1/3 for m

`m_2 = -(1)/(1/3)`

Express as a proper division

`m_2 = -1/ (1)/(3)`

Convert to *

`m_2 = -1* (3)/(1)`

`m_2 = -(3)/(1)`

`m_2 = -3`