Question

If the straight line , 2x-5y +4 =0 is perpendicular to the line passing through the point (1,5) and (a,3), then a equals

• A. 6/5
• B. 9/5
• C. 7/8
• D. 2

Answer 1

Answer:

B. 9/5

let the slope of the line 2x-5y+4=0 be $m_1$ and the slope of the line joining the points (1,5) and (a,3) be $m_2$

$m_2=\frac{3-5}{a-1}=\frac{-2}{a-1}$

now, the slope of the line = $m_1=\frac{2}{5}$

given lines are perpendicular to each other

$m_1m_2=-1$

$\frac{-2}{a-1}\times\frac{2}{5}=-1$

$a-1=\frac{4}{5}$

$a=\frac{4}{5}+1=\frac{9}{5}$