find the coordinates of point equidistant from the points A (1,2) B (3,-4) C (5,-6)

Let point D(x, y) is equidistant from A(1, 2), B(3, - 4), C(5, - 6) 

∴ AD = BD = CD.

we can calculate the distance between two points using distance formula.

take AD = BD

  ()

  (taking common 4)  ... (1)

now take BD = CD

  (by taking 4 common)  ... (2)

now subtract equation (2) from equation (1)

y = 2

put the value of y in equation (1)

x = 11

Hence the point D(11,2) is equidistant from A, B, C.

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