Respuesta :
Given:
The slope of a line l is [tex]\dfrac{12}{11}[/tex].
To find:
The pair of points of a line which is perpendicular to the line l.
Solution:
If the slope of a line is [tex]m[/tex], then the slope of the line which is perpendicular to the line is [tex]-\dfrac{1}{m}[/tex].
The slope of a line l is [tex]\dfrac{12}{11}[/tex]. So, the slope of the perpendicular line is [tex]-\dfrac{11}{12}[/tex].
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
In option A, the pair of points is (21,−4) and (−5,7).
[tex]m_1=\dfrac{7-(-4)}{-5-21}[/tex]
[tex]m_1=\dfrac{11}{-26}[/tex]
In option B, the pair of points is (−7,−5) and (4,7).
[tex]m_2=\dfrac{7-(-5)}{4-(-7)}[/tex]
[tex]m_2=\dfrac{12}{11}[/tex]
In option C, the pair of points is (7,−7) and (−5,4).
[tex]m_3=\dfrac{4-(-7)}{-5-7}[/tex]
[tex]m_3=\dfrac{11}{-12}[/tex]
[tex]m_3=-\dfrac{11}{12}[/tex]
In option D, the pair of points is (−2,−5) and (4,7).
[tex]m_4=\dfrac{7-(-5)}{4-(-2)}[/tex]
[tex]m_4=\dfrac{12}{6}[/tex]
[tex]m_4=2[/tex]
The slope of the line is [tex]-\dfrac{11}{12}[/tex] if the line passes through the points (7,−7) and (−5,4).
Therefore, the correct option is C.
