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Question
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 )`.
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