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


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) $(0,3)$



Let P(x, 0) be the point on x-axis. Then as per the question

$A P=B P \Rightarrow A P^{2}=B P^{2}$


$\Rightarrow x^{2}-14 x+49+36=x^{2}+6 x+9+16$

$\Rightarrow 60=20 x$

$\Rightarrow x=\frac{60}{20}=3$

Thus, the required point is (3, 0).
Hence, the correct answer is option (c).


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