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Geometry Smart Math

[Smart Math] Geometry Problem 1

Here’s and example of a SMART MATH problem for GEOMETRY.

Geometry

Problem

Find the distance between points P (-3, 2) and Q (-5, 8).

  1. \sqrt{40}units
  2. 4 units
  3. 6 units
  4. \sqrt{60}units
  5. \sqrt{30}units

The Usual Method

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Using formula of distance between two points = \sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}

= \sqrt{((-3)-(-5))^{2}+((2)-(8))^{2}}

= \sqrt{4+36}

= \sqrt{40} units

(Ans: 1)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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Difference between x_{1}and x_{2}= 2 units

Difference between y_{1}and y_{2}= 6 units

Since, the lines PQ, (x_{1}-x_{2}) and (y_{1}-y_{2})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 \sqrt{40} \approx 6.3 units.

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
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