question_answer

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

A)  (2, 0)                    

B)         (0, 3)

C)  (-2, 2)                  

D)         (3, 0)

Correct Answer: A

Solution :

 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\[\Rightarrow \]. Let A and B denote the points (5, 4) and (-2, 3) respectively. Given that AP = BP, we have \[\frac{x-4}{4}=\frac{3x-19}{x-3}\] i.e., \[\Rightarrow \] \[x=11\,or\,8\] \[\therefore \] \['x'\] Thus, the required point is (2, 0).