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Question

Find the distance between the following pair of points.
$$(a, b)$$ and $$(-a, -b)$$.


Solution

$$\begin{matrix} (a_{ { x_{ 1 } } },b_{ { y_{ 1 } } })and\left( { { -a }_{ \, \, \, \, \, \, \, { x_{ 2 } } },-b_{ { y_{ 2 } } } } \right)  \\ As\, we\, know\, that\, from\, dis\tan  ce\, formula \\ \Rightarrow \sqrt { { { \left( { { x_{ 2 } }-{ x_{ 1 } } } \right)  }^{ 2 } }{ { \left( { { y_{ 2 } }-{ y_{ 1 } } } \right)  }^{ 2 } } } \,  \\ \Rightarrow Dis\tan  ce\, b/w\, po{ int }s=\sqrt { { { \left( { -a-a } \right)  }^{ 2 } }+{ { \left( { -b-b } \right)  }^{ 2 } } }  \\ \Rightarrow Dis\tan  ce\, b/w\, po{ int }s=\sqrt { { { \left( { -2a } \right)  }^{ 2 } }-{ { \left( { -2b } \right)  }^{ 2 } } }  \\ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =\sqrt { 4{ a^{ 2 } }+4{ b^{ 2 } } }  \\ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =2\sqrt { { a^{ 2 } }+{ b^{ 2 } } } \, unit \\  \end{matrix}$$

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