Find a point on the X-axis which is equidistant from the points (5,4) and (−2,3).
Let the point on the x-axis be (x,0)
Distance between (x,0) and (5,4)=√(5−x)2+(4−0)2=√52+x2−10x+16=√x2−10x+41
Distance between (x,0) and (−2,3)=√(−2−x)2+(3−0)2=√22+x2+4x+9=√x2+4x+13
As the point (x,0) is equidistant from the two points, both the distances calculated are equal.
√x2−10x+41=√x2+4x+13
=>x2−10x+41=x2+4x+13
41−13=10x+4x
28=14x
x=2. Thus, the point is (2,0).