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Question
The line through A(–2, 3) and B(4, b) is perpendicular to the line 2x – 4y = 5. Find the value of b.
Solution
Slope of the line through A(–2, 3) and B(4, b) = `m_1 = (y_2 - y_1)/(x_2 - x_1) = (b - 3)/(4+2) = (b -3)/6`
Equation of given line is 2x - 4y - 5 = 0
`=> 4y = 2x - 5`
`=> y = 1/2 x - 5/4`
∴ Slope of given line = `m_2 = 1/2`
Since the lines are perpendicular therefore `m_1 xx m_2 = -1`
`=> (b - 3)/6 xx 1/2 = -1`
`=> b -3 = -12 => b = -9`
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