Find the points on the X - axis which are at a distance of from the point (7, - 4). How many such points are there?


We know that, every point on the X - axis in the form (x, 0).

Let P(x, 0) the point on the X - axis have distance from the point Q(7, - 4).


As we know;


Distance between the points (x1, y1) and (x2, y2);


d =


By given condition,


Distance of PQ =


(PQ)2 = 4 × 5


(x – 7)2 + (0 + 4)2 = 20


x2 + 49 - 14x + 16 = 20


x2 - 14x + 65 - 20 = 0


x2 - 14x + 45 = 0


x2 - 9x – 5x + 45 = 0


By Factorization method:


x(x - 9) – 5(x – 9) = 0


(x – 9)(x – 5) = 0


x = 5, 9


Hence, there are two points lies on the axis, which are (5, 0) and (9, 0), have distance from the point (7, - 4).


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