Question

the point on the x-axis which is equidistant from the point A(-2,5) and B(2,-3) is

Answer 1

Let the Point on X - Axis be : (P , 0)

Given : This Point (P , 0) is Equidistant from the Points A(-2 , 5) and B(2 , -3)

⇒ Distance Between Point A and Point P should be Equal to Point A and Point B (i.e. PA = PB)

We know that : Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

$\heartsuit$  $\bold{D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Given : Point A : (-2 , 5) and Point B : (2 , -3)

$\bold{\implies \sqrt{(P + 2)^2 + (5)^2} = \sqrt{(P - 2)^2 + (-3)^2}}$

$\bold{Squaring\;on\;Both\;Sides,\;We\;get :}$

$\bold{\implies (P + 2)^2 + 25 = (P - 2)^2 + 9}$

$\bold{\implies (P^2 + 4) + 4P + 16 = (P^2 + 4) - 4P}$

$\bold{\implies 8P = -16}$

$\bold{\implies P = -2}$

So, The Point on X - Axis which is Equidistant from the given point is :

$\heartsuit$  (-2 , 0)