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Find the distance between the following pairs of points (i)((2,3),(4,1))

Question

Find the distance between the following pairs of points
(i)\((2,3),(4,1)\)

Answer

\(2\sqrt2\) unit 
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Solution

 Let \(A(2,3)\)and \(B(4,1)\)  be the given points.
Here \(x_{1}=2,y_{1}=3\)and \(x_{2}=4,y_{2}=1\)
\(\therefore \) \(AB=\sqrt {(x_{2}-{x_{1}})^{2}+(y_{2}-y_{1})^{2}}\)
\(=\sqrt {(4-2)^{2}+(1-3)^{2}}\)
\(=\sqrt {(2)^{2}+(-2)^{2}}\)
\(=\sqrt {4+4}\)
\(=\sqrt {8}=2\sqrt {2}\)unit 
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