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