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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
The slope of the line passing through two given points A(x1, y1) and B(x2, y2) is
Slope of AB = `(y_2 - y_1)/(x_2 - x_1)`
The slope of the line passing through two
Given points A(−2, 3) and B(4, b) is
Slope of AB = `(b - 3)/(4 - (-2)) = (b - 3)/(4 + 2) = (b - 3)/6`
Equation of the given line is 2x – 4y = 5
`=>` Equation is 4y = 2x – 5
`=>` Equation is `y = 1/4 (2x - 5)`
`=>` Equation is `y = x/2 - 5/4`
Comparing this equation with the general equation,
Y = mx + c, we have m = `1/2`
Since the given line and AB are perpendicular to each other, the product of their slopes is –1
∴ `((b-3)/6) xx 1/2 = - 1`
`=>` b – 3 = –12
`=>` b = 3 – 12
`=>` b= –9
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