Question

The line through $A(-2,3)$ and $B(4,b)$ is perpendicular to the line $2x-4y=5$. Find the value of $|b|$.

Answer 1

The slope of line $AB$ is $\frac{b-3}{4+2}=\frac{b-3}{6}$

Again, slope of line $2x-4y=5$ is $\frac{1}{2}$

Since line $AB$ is perpendicular to $2x-4y=5$

$m_1{m}_2=-1$

$\Rightarrow \frac{b-3}{6}\times \frac{1}{2}=-1$

$\Rightarrow b-3=-12$

$\Rightarrow b=-9$

Hence $|b|=9$