Question

Find the distance between the points (2,3) and (4,1)​

Answer 1

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\green{AnswEr:-}}}$

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• The distance between the points = √8

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$\sf{\underline{\green{Given:-}}}$

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• The given points are (2,3) and (4,1).

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$\sf{\underline{\green{Find:-}}}$

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• The distance between the points = ?

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$\sf{\underline{\green{Explanation:-}}}$

$\sf{\underline\purple{Formula\:Used\:Here:-}}$

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$\bigstar\boxed{\sf{\red{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}$

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$\sf{\underline{\pink{Putting\:the\:values:-}}}$

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$\dashrightarrow \sf {Distance = \sqrt{(4-2)^2 + (1-3)^2}}$

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$\dashrightarrow \sf {Distance = \sqrt{2^2 + (-2)^2} }$

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$\dashrightarrow \sf {Distance = \sqrt{4 + 4} }$

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$\dashrightarrow{\gray{ \underbrace{\boxed{\underline{\underline{\blue{ \tt Distance\: between\:the\: points = \sqrt{8} }}}}}}}$

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$\:\:\:\:\dag\bf{\underline{\underline \red{Hence:-}}}$

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• The distance between the points = √8

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$\rule{200}{2}$

Answer 2

SOLUTION

TO DETERMINE

The distance between the points (2,3) and (4,1)

FORMULA TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

EVALUATION

Here the given points are (2,3) and (4,1)

The distance between the points (2,3) and (4,1)

$\sf = \sqrt{ {(4 - 2)}^{2} + {(1 - 3)}^{2} } \: \: unit$

$\sf = \sqrt{ {(2)}^{2} + {( - 2)}^{2} } \: \: unit$

$\sf = \sqrt{4 + 4 } \: \: unit$

$\sf = \sqrt{8 } \: \: unit$

$\sf = \sqrt{2 \times 2 \times 2 } \: \: unit$

$\sf = \sqrt{ {2}^{2} \times 2 } \: \: unit$

$\sf = 2 \sqrt{ 2 } \: \: unit$

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