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in Coordinate Geometry by (44.5k points)
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Find the point on x - axis which is equidistant from the following pair of points:  (3, 2) and (- 5, - 2)

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Given points are A(3, 2) and B(- 5, - 2).

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 - 3)2 + (0 - 2)2 = (x + 5)2 + (0 - (- 2))2

⇒ (x - 3)2 + (- 2)2 = (x + 5)2 + (2)2

⇒ x2 - 6x + 9 + 4 = x2 + 10x + 25 + 4

⇒ 16x = - 16

⇒ x = -16/16

⇒ x = - 1

∴ The point on x - axis is (- 1, 0).

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