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Question

# Find the distance between each pair of points. If necessary, round answers to two decimal places. (-2, 3) and (3, -9)

Solution

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Let $x_{1}=-2 \ , \ x_{2}=3$      and $y_{1}=3 \ , \ y_{2}=-9$

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$      $\quad {\color{#4257b2}The distance form}$

$d=\sqrt{(3-(-2))^{2}+(-9-3)^{2}}$      $\quad {\color{#4257b2}Substitute the given values}$

$d=\sqrt{(5)^{2}+(-12)^{2}}$      $\quad {\color{#4257b2} 3-(-2)=5 \ and -9-3=-12}$

$d=\sqrt{25+144}$      $\quad {\color{#4257b2} $5^{2}=25$ \ and $(-12)^{2}=144$}$

$d=\sqrt{169}$

=13 length unit

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