Question

Find the coordinates of point which are equidistant from these two points P(3,0) and Q(-3,0). How many points are possible satisfying this condition?

Answer 1

Given

we need to find the coordinates of a point which are equidistant from the points P (3,0) and Q (- 3,0)

Analysis

From the graph each point on y axis is equidistant from the two points P(3,0) and Q (- 3, 0)

Now the origin (0,0) is 3 units away from the given points P(3,0) and Q (-3,0)

applying,

distance formula we have

So d = √(x2 – x1)^2 + (y2 – y1)^2

         = √0 – (-3)^2 + (1 – 0)^2

         = √3^2 + 1^2

         = √10

   So the point (0,1) is equidistant from P(-3,0). Now d = √10 and so similarly any point that lies on y axis is equidistant from p(3,0) and q(- 3,0)

hence

there are infinite number of co-ordinates that are equidistant from point P(3,0) and q(-3,0)