Question

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

• A. 6
• B. -6
• C. 9
• D. -9

Answer 1

The correct option is D

-9

Slope of AB $=\frac{b-3}{4+2}=\frac{b-3}{6}=m_1$ and $2x-4y=5\Rightarrow 4y=2x-5$
$\Rightarrow y=\frac{1}{2},x-\frac{5}{4}$
$\therefore m_2=\frac{1}{2}$
As the lines are perpendicular, $m_1{m}_2=-1$
$\therefore m_1=-\frac{1}{m_2}$
$\Rightarrow \frac{b-3}{6}=-\frac{1}{\frac{1}{2}}$
$\Rightarrow \frac{b-3}{6}=-2$
$b-3=-12\Rightarrow b=-9$