Question

The point on the X-axis which is equidistant from (5,4) and (2,3) has the coordinates .

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

Answer 1

The correct option is A $(\frac{14}{3},0)$

Any point on the x axis has its y coordinate 0.
Let the point have the coordinates (x,0)

The point is equidistant from (5,4) and (2,3).

This means that the square of the distance of the point from the given points is equal.

$(5-x{)}^2+(4-0{)}^2=(2-x{)}^2+(3-0{)}^2$
$\Rightarrow x^2-10x+25+16=x^2-4x+4+9$
$\Rightarrow 41-10x=13-4x$
$\Rightarrow 6x=28$
$\Rightarrow x=\frac{28}{6}=\frac{14}{3}$

Thus, the required coordinates are $(\frac{14}{3},0)$