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Find the distance between the points (a, b) and (−a, −b).

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#### Solution

Using distance formula:

d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 )`

Here, x_{1} = a, y_{1} = b, x_{2} = - a and y_{2 }= - b

On substituting the values in the formula we get

= `sqrt(( - a - a)^2 + ( - b - b)^2)`

= `sqrt((- 2a)^2 + (-2b)^2)`

= `sqrt( 4a^2 + 4b^2)`

= `2sqrt(a^2 + b^2 )`

Therefore, the distance between (a, b) and (−a,−b) is `2sqrt(a^2 + b^2 )`.

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