Question

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

Answer 1

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