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Find the Distance Between the Points (A, B) and (−A, −B). - Mathematics

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Sum

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, x1 = a, y1 = b, x2 = -a and y2 = -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))`

Concept: Heights and Distances
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