Question

The point on the x- axis which is equidistant from the points $(7,6)$ and $(-3,4)$ is

• A. $(0,3)$
• B. $(3,0)$
• C. $(-3,0)$
• D. $(0,-3)$

Answer 1

The correct option is B $(3,0)$

Let the point on the x-axis be $(x,0)$.

Distance between $(x,0)$ and $(7,6)=\sqrt{{(7-x)}^2+{(6-0)}^2}=\sqrt{49+x^2-14x+36}=\sqrt{x^2-14x+85}$

Distance between $(x,0)$ and $(-3,4)=\sqrt{{(-3-x)}^2+{(4-0)}^2}=\sqrt{9+x^2+6x+16}=\sqrt{x^2+6x+25}$

As the point $(x,0)$ is equidistant from the two points, both the distances calculated are equal.

$\sqrt{x^2-14x+85}=\sqrt{x^2+6x+25}$

$=>x^2-14x+85=x^2+6x+25$

$85-25=6x+14x$

$60=20x$

$x=3$

Thus, the point is $(3,0)$.