Question

Find the distance of the point (3,5) from line 2x + 3y = 14 measured parallel to a line having slope 1/2

Answer 1

Equation of AB:-

$y-5=\frac{1}{2}(x-3)$

$\Rightarrow 2y-10=x-3$

$\Rightarrow 2y=x+7$

Intersection with l:-

$2(2y-7)+3y=14$

$\Rightarrow 7y=28$

$\Rightarrow y=4$

$\Rightarrow x=1$

$\Rightarrow B(1,4)$

Distance between A and B:-

$\sqrt{(3-1{)}^2+(5-4{)}^2}=\sqrt{4+1}=\sqrt{5}$.