Find the distance between points P (-3, 2) and Q (-5, 8).
The Usual Way
Using formula of distance between two points =
Estimated Time to arrive at the answer = 30 seconds.
The Smart Way
Difference between and = 2 units
Difference between and = 6 units
Since, the lines PQ, and form a right angled triangle with PQ as the hypotenuse. We already know that the hypotenuse of any right triangle should be more than the longest right side but less than the sum of the right sides. Thus length of PQ should be lying between 6 < PQ < (6 + 2). The only value satisfying this range is 6.3 units.
Estimated Time to arrive at the answer = 15 seconds.