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in Mathematics by (65.0k points)

Find a point on the X-axis which is equidistant from the points (5, 4) and (-2, 3).

1 Answer

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Best answer

Since the required point (say P) is on the X-axis, its ordinate will be zero. Let the abscissa of the point be x.

Therefore, coordinates of the point P are (x, 0).

Let A and B denote the points (5, 4) and (-2, 3), respectively.

Since we are given that AP = BP, we have AP2 = BP2

i.e., (x - 5)2 + (0 - 4)2 = (x + 2)2 + (0 - 3)2

or x2 + 25 - 10x + 16 = x2 + 4 + 4x + 9 or -14x = - 28 or x = 2

Thus, the required point is (2, 0).

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