A line through A(-2,6) and B(4,b) is perpendicular to the line 2x - 4y = 5. The value of b is ___.

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Solution

Slope of the line AB = $\frac{b - 6}{4 + 2}$

= $\frac{b - 6}{6}$

Slope of line $2 x - 4 y = 5$ is

$- 4 y = - 2 x + 5$

$y = \frac{1}{2} x - \frac{5}{4}$ [ slope is $\frac{1}{2}$ ]

Since the lines are perpendicular

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

$\Rightarrow b - 6 = - 12 o r b = - 6$

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