Question

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

Solution

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

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