Question

Find a point on the $x$-axis, which is equidistant from the points (5, 4) and (2, 3).

• A. $(\frac{15}{2},0)$
• B. $(\frac{14}{3},0)$
• C. $(\frac{27}{7},0)$
• D. $(\frac{10}{3},0)$

Answer 1

The correct option is B

$(\frac{14}{3},0)$

Let point $(x,0)$ is the point on the x-axis that is equidistant from the points (5, 4) and (2, 3).

Accordingly,

$\sqrt{(5-x{)}^2+(4-0{)}^2}=\sqrt{(2-x{)}^2+(3-0{)}^2}$

Squaring on both sides, we get,

$5^2+x^2-10x+16=4+x^2-4x+9$

$41-10x=13-4x$

$-6x=-28$

$x=\frac{14}{3}$

Thus, required point on the x-axis is $(\frac{14}{3},0)$