Given points P(2,3), Q(4,-2), and R(a,0). Find the value of 'a' if |PR - RQ| is maximum.

There is an X axis and there’s a Y axis, and the point P (2,3) and Q (4, -2) lie in the first and fourth Quadrant respectively. The Point R (a, 0) lies on the X axis.

Since the y co-ordinate of P is 3 and y co-ordinate of Q is -2, point Q is obviously closer to X axis than point P, if you take a perpendicular distance between the points (individually) and the X axis.

Now, if you calculate the square of the difference between PR and RQ (PR - RQ), you get 4a - 7. It’s easy to observe that the value of 4a - 7 will keep on increasing as ‘a’ increases. In view of this, we can’t possibly calculate maximum value of |PR-RQ|.

Hope this helps.