Question

Find the coordinates of the point on the x-axis which is equidistant from the points P(-2, -5) and Q(2, 3).

• A. (3 , 0)
• B. (-3 , 0)
• C. (-2 , 0)
• D. (2 , 0)

Answer 1

The correct option is C (-2 , 0)

Let the Point A$(x,0)$ on X-axis be equidistant from P(-2,-5) and Q(2,3).

$\therefore PA=PQ\Rightarrow P{A}^2=P{Q}^2$

Distance, $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$(x-(-2){)}^2+(0-(-5){)}^2=(x-2{)}^2+(0-3{)}^2(x+2{)}^2+(5{)}^2=(x-2{)}^2+(-3{)}^2{x}^2+4x+4+25=x^2-4x+4+98x+25=98x=9-25=-16x=-2$

Co-ordinates of point on X-axis is $(-2,0)$