Find the point on x - axis which is equidistant from the following pair of points:

(7, 6) and (- 3, 4)


Given points are A(7, 6) and B(- 3, 4).



We need to find a point on x - axis which is equidistant from these points.


Let us assume the point on x - axis be S(x, o).


We know that distance between the points (x1, y1) and (x2, y2) is .


From the problem,


⇒ SA = SB


⇒ SA2 = SB2


⇒ (x - 7)2 + (0 - 6)2 = (x - (- 3))2 + (0 - 4)2


⇒ (x - 7)2 + (- 6)2 = (x + 3)2 + (- 4)2


⇒ x2 - 14x + 49 + 36 = x2 + 6x + 9 + 16


⇒ 20x = 60



⇒ x = 3


∴ The point on x - axis is (3, 0).


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