Question

Which point on x-axis is equidistant from the points A(7, 6) and B(−3, 4)?
(a) (0, 4) (b) (−4, 0) (c) (3, 0) (d) (0, 3)

Answer 1

Let P(x, 0) be the point on x-axis. Then as per the question
$$\begin{gathered} AP=BP\Rightarrow A{P}^2=B{P}^2 \\ \Rightarrow {\left(x-7\right)}^2+{\left(0-6\right)}^2={\left(x+3\right)}^2+{\left(0-4\right)}^2 \\ \Rightarrow x^2-14x+49+36=x^2+6x+9+16 \\ \Rightarrow 60=20x \\ \Rightarrow x=\frac{60}{20}=3 \end{gathered}$$
Thus, the required point is (3, 0).
Hence, the correct answer is option (c).