Question

What point on the 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

(c) (3, 0)
Let P(x,0) be equidistant from the points A(7,6) and B(−3,4).
Then,
$$\begin{gathered} PA=PB \\ \Rightarrow P{A}^2=P{B}^2 \\ \Rightarrow {\left(x-7\right)}^2+{\left(0-6\right)}^2={\left(x+3\right)}^2+{\left(0-4\right)}^2 \\ \Rightarrow x^2-14x+49+36=x^2+6x+9+16 \\ \Rightarrow x^2-14x+85=x^2+6x+25 \\ \Rightarrow 20x=60 \\ \Rightarrow x=3\text{units} \end{gathered}$$
Hence,
$\left(x=3,y=0\right)\Rightarrow \left(3,0\right)$