For the figure given below, A(3, 0) is the midpoint of the line joining P(3, 3) and Q(3, -3).
If the point (3,0) is the midpoint of the line joining (3,3) and (3,-3), then, it is equidistant from both the points.
AP=√(3−3)2+(3−0)2=3−−−−−−−−−−−−−−− (1)AQ=√(3−3)2+(−3−(0))2=3−−−−−−−−−−−−−−− (2)
From (1) and (2),
AP = AQ.
The line joining P and Q is x = 3. This is because the x coordinates of P and Q are equal to 3. So, the points P and Q lie on the line in which any point has its x coordinate equal to 3. Point A also lies on the same line x =3.
Since point A lies on the line joining P and Q, and A is equidistant from P and Q, A is the mid point of P and Q.