A is a point on x-axis, B = (5, -4) and AB = 5 units, find the co-ordinates of A.

Let the point A be (a, 0).

AB = 5 units

Distance between 2 points (x₁, y₁) and (x₂, y₂) = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Distance between A = (a, 0) and B = (5, -4) =

$\Rightarrow 5 = \sqrt{(5 - a)^2 + (-4 - 0)^2}\\[1em] \Rightarrow 5^2 = (5 - a)^2 + (-4)^2\\[1em] \Rightarrow 25 = 25 + a^2 - 10a + 16\\[1em] \Rightarrow a^2 - 10a + 16 + 25 - 25 = 0\\[1em] \Rightarrow a^2 - 10a + 16 = 0\\[1em] \Rightarrow a^2 - 8a - 2a + 16 = 0\\[1em] \Rightarrow a(a - 8) - 2(a - 8) = 0\\[1em] \Rightarrow (a - 8)(a - 2) = 0\\[1em] \Rightarrow (a - 8) = 0 \text{ or } (a - 2) = 0\\[1em] \Rightarrow x = 8 \text{ or } x = 2\\[1em]$

Hence, the co-ordinates of point A = (8, 0) or (2, 0).