Question

Write the coordinates of a point P on x-axis which is equidistant from the point A(–2, 0) and B(6, 0).

Answer 1

Let coordinates of a point P on x-axis be P(x, 0).

Thus, AP = BP
$$\begin{gathered} \Rightarrow {\left(AP\right)}^2={\left(BP\right)}^2 \\ \Rightarrow {\left(\sqrt{{\left(x-\left(-2\right)\right)}^2+{\left(0-0\right)}^2}\right)}^2={\left(\sqrt{{\left(x-6\right)}^2+{\left(0-0\right)}^2}\right)}^2 \\ \Rightarrow {\left(x+2\right)}^2+{\left(0\right)}^2={\left(x-6\right)}^2+{\left(0\right)}^2 \\ \Rightarrow {\left(x+2\right)}^2={\left(x-6\right)}^2 \\ \Rightarrow x^2+4+4x=x^2+36-12x \\ \Rightarrow 4x+12x=36-4 \\ \Rightarrow 16x=32 \\ \Rightarrow x=2 \\ \mathrm{Therefore},x=2. \end{gathered}$$

Hence, the coordinates of a point P on x-axis are (2, 0).