Question

Answer the following question:

P(a, b) is the mid point of a line segment between axes. Show that the equation of the line is `x/"a" + y/"b"` = 2

Answer 1

Let the intercepts of a line AB be x₁ and y₁ on the X and Y-axes respectively.

∴ A ≡ (x₁, 0), B ≡ (0, y₁)

P(a, b) is the midpoint of a line segment AB intercepted between the axes.

∴ P = `(("x"_1+0)/2,(0+"y"_1)/2)`

∴ (a, b) = `("x"_1/2,"y"_1/2)`

∴ a = `"x"_1/2`

∴ x₁ = 2a

and b = `"y"_1/2`

∴ y₁ = 2b

∴ Equation of the required line AB is

`"x"/"x"_1+"y"/"y"_1` = 1

∴ `"x"/(2"a")+"y"/(2"b")` = 1

∴ `"x"/"a" + "y"/"b"` = 2