Question

A line passing through the points (a,2a) and (-2,3) is perpendicular to the 4x+3y+5=0 find the value of a

Answer 1

Given ,

A line passing through the points (a,2a) and (-2,3) is perpendicular to the 4x+3y+5=0

We know that ,

The slope of the two points is given by

$\large \sf \fbox{m = \frac{ y_{2} - y_{1} }{x_{2} - x_{1}} }$

Thus ,

m = (3 - 2a)/(-2 - a)

Now , slope of the line 4x + 3y + 5 = 0

3y = - 4x - 5

y = (-4/3)x + (-5/3)

Thus , the slope of the given line is -4/3

On comparing with y = mx + c , we get

m = -4/3

We know that , if two lines are perpendicular to each other then

$\large \sf \fbox{m_{1} \times m_{2} = - 1}$

Thus ,

$\sf \mapsto ( \frac{3 - 2a}{-2 - a} ) \times ( - \frac{4}{3} ) = - 1 \\ \\\sf \mapsto - 12 + 8a = 6 + 3a \\ \\\sf \mapsto 5a = 18 \\ \\ \sf \mapsto a = \frac{18}{5}$

$\therefore{\sf \underline{The \: value \: of \: a \: is \: \frac{18}{5} }}$