Question

Line l has a slope of 12/11. The line through which of the following pair of points is perpendicular to l

A. (21,−4),(−5,7)
B. (−7,−5),(4,7)
C. (7,−7),(−5,4)
D. (−2,−5),(4,7)

Answer 1

C

Explanation:

its c

Answer 2

Given:

The slope of a line l is
`(12)/(11)`.

To find:

The pair of points of a line which is perpendicular to the line l.

Solution:

If the slope of a line is
`m`, then the slope of the line which is perpendicular to the line is
`-(1)/(m)`.

The slope of a line l is
`(12)/(11)`. So, the slope of the perpendicular line is
`-(11)/(12)`.

Slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

In option A, the pair of points is (21,−4) and (−5,7).

`m_1=(7-(-4))/(-5-21)`

`m_1=(11)/(-26)`

In option B, the pair of points is (−7,−5) and (4,7).

`m_2=(7-(-5))/(4-(-7))`

`m_2=(12)/(11)`

In option C, the pair of points is (7,−7) and (−5,4).

`m_3=(4-(-7))/(-5-7)`

`m_3=(11)/(-12)`

`m_3=-(11)/(12)`

In option D, the pair of points is (−2,−5) and (4,7).

`m_4=(7-(-5))/(4-(-2))`

`m_4=(12)/(6)`

`m_4=2`

The slope of the line is
`-(11)/(12)` if the line passes through the points (7,−7) and (−5,4).

Therefore, the correct option is C.