Question

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

Answer 1

Step-by-step explanation:

here the given points are (a,b) and

(-a,-b).

let us consider,

A ( a, b) = ( x1 , y1 )

B ( - a, - b) = (x2 , y2 )

we know the distance formula,

distance = √ [( y2 - y1)² + (x2 - x1)²]

therefor

the distance between the points A and B = √ [ (- b - b)² + (-a - a) ²]

AB = √ [ ( -2b)² + (-2a )² ]

= √ [ 4b² + 4a² ]

= √ [ 4 ( a ² + b² ) ]

= 2 √ ( a² + b² )

therefor the between two given points is 2 √ ( a² + b² )

Answer 2

Answer:

$2 \sqrt{a ^{2} + {b}^{2} }$

Step-by-step explanation:

Let

$(x_1, y_1), (x_2,y_2) \:$ are two points. The distance between them is given by,

$\sqrt{(x_2 - x_1) ^{2} + (y_2 - y_1)^{2} }$

Given,

$(x_1, y_1) = (a, b) \\ (x_2,y_2) =( - a, - b)$

So, Distance between them is

$= \sqrt{( - a - a) ^{2} + ( - b - b) ^{2} } \\ = \sqrt{( - 2a) ^{2} + { (- 2b)}^{2} } \\ = \sqrt{4 {a}^{2} + 4 {b}^{2} } \\ = \sqrt{4( {a}^{2} + {b}^{2}) } \\ = 2 \sqrt{( {a}^{2} + {b}^{2})}$

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