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.