Question

the point P on x axis equidistant from the points A(-1,0) and B(5,0) is​

Answer 1

Answer:

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Answer 2

$\fontsize{18}{10}{\textup{\textbf{The required point P is (2, 0).}}}$

Step-by-step explanation:

Let (x, 0) be the co-ordinates of the point P on X-axis that is equidistant from the points A(-1, 0) and B(5, 0).

Then, we must have

$PA=PB\\\\\Rightarrow \sqrt{(-1-x)^2+(0-0)^2}=\sqrt{(5-x)^2+(0-0)^2}\\\\\Rightarrow 1+2x+x^2=25-10x+x^2~~~\textup{[Squaring both sides]}\\\\\Rightarrow 2x+10x=25-1\\\\\Rightarrow 12x=24\\\\\Rightarrow x=\dfrac{24}{12}\\\\\Rightarrow x=2.$

Thus, the required point P is (2, 0).