Question

find the value of a if the line through (-2,3)and(8,5)is perpendicular to y=ax+2​

Answer 1

$\textbf{Given:}$

$\text{Line joining (-2,3) and (8,5 is perpendicular to y=a\,x+2 }$

$\textbf{To find:}$

$\text{The value of 'a'}$

$\textbf{Solution:}$

$\text{slope of the line joining (-2,3) and (8,5)}=m_1$

$=\dfrac{y_2-y_1}{x_2-x_1}$

$=\dfrac{5-3}{8+2}$

$=\dfrac{2}{10}$

$=\dfrac{1}{5}$

$\text{By comparing y=a\,x+2 with y=m\,x+c we get}$

$\text{Slope,}\,m_2=a$

$\text{Since the line joining (-2,3) and (8,5) and the line y=a\,x+2 are perpendicular,}$

$\text{We have}$

$m_1{\times}m_2=-1$

$\dfrac{1}{5}{\times}a=-1$

$\implies\bf\,a=-5$

$\textbf{Answer:}$

$\textbf{The value of a is -5 }$

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