The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.
$[2 M a r k s]$

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Solution

Slope of AB $= \frac{b - 3}{4 + 2} = \frac{b - 3}{6} = m_{1}$ and $2 x - 4 y = 5 \Rightarrow 4 y = 2 x - 5$
$\Rightarrow y = \frac{1}{2}, c = - \frac{5}{4}$
$∴ m_{2} = \frac{1}{2}$
$[1 M a r k]$
As the lines are perpendicular, $m_{1} m_{2} = - 1$
$∴ m_{1} = - \frac{1}{m_{2}}$
$\Rightarrow \frac{b - 3}{6} = - \frac{1}{\frac{1}{2}}$
$\Rightarrow \frac{b - 3}{6} = - 2$
$b - 3 = - 12 \Rightarrow b = - 9$
$[1 M a r k]$

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